MAGNETO-OPTIC TRAP

A POSITRON DETECTOR FOR PRECISION

BETA DECAY EXPERIMENTS FROM A

MAGNETO-OPTIC TRAP

Dan G. Melconian B.Sc., MCMaster University, 1995

A thesis submitted in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE in the

Department of P hysics

@ Dan G. Melconian 2000 SIMON FRASER UNIVERSITY

July 2000

Copyrights are not reserved. Permission is hereby granted to

reproduce this work in whole or in part.

sitions and Acquisitions et B' iogiaphic Senrices senrices bibliographiques "ds"

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Abstract

The TRINAT collaboration has rnagneto-optically trapped 38mK from TRIU~IF'S ra-

dioactive beam facility with the goal of measuring to better than 1% the b - t~ cor-

relation parameter, a, of the superallowed P decay. This measurement will test the

Standard Mode1 prediction of a = +l, where a deviation from unity wvould be a clear

indication of scalar contributions to the weak interaction.

The subject of this thesis is the design, optimization and characterization of a

plastic scintillator used in coincidence with a double-sided Si-strip detector to observe

the E and AE of the emitted positron. The timing response of the scintillator relative

to a rnicrechannel plate has a width of o = 1 ns, which provides a good time-of-flight

measurement used to determine the recoil momentum, allowing that of the neutrino

to be deduced.

The scintillator was designed with the aid of Monte Carlo simulations and opti-

mized for the O - 5 MeV region oE interest. The energy has been calibrated to within

f 5 keV using the Compton edges of y sources as well as by the on-line B spectrum.

The gain of the scintillator is kept constant over the course of the experiment to within

0.15% by a stabilization system.

The silicon strip detector has been calibrated using photon sources (30-80 keV)

and the calibration was extended using the on-line data by requiring energy agree-

ment between the 2 and jj strips. Using these calibrations, a detailed analysis scheme

has been developed that accounts for charge sharing between strips and multiple hits.

The strip detector is an important component of the telescope because it provides an

effective tag for B events which are needed to discriminate against the 38K Y back-

ground in the scintiiiator. A hardware coincidence behveen the E and A E detectors

reduces this background by a factor of 35, and the analysis scheme reduces it another

order of magnitude with minimal loss of good P events.

The P telescope's energy spectrum from the April-May 1999 experirnental run is well reproduced by detailed simulations above 2.5 MeV, the lowest P energy ex-

pected to be used in the analysis of a. The simulations are not quite as accurate in

reproducing the background and the Compton summing of the annihilation radiation,

limiting our understanding of the lower-energy part of the 0 spectrum. A coincidence

condition with the recoil detector, however, virtually eliminates these backgrounds,

providing a clean measurement for the correlation experiment.

In memory of Otto Hausser

There are grounds for cautious optimism that Ive may now be near the

end of the search for the ultimate laws of nature.

Stephen Hawking

A Brief Histoy of Time, 1988

Acknowledgement s

1 would like to thank first and foremost the late Prof. Otto Hausser for providing

me with the wonderful opportunity of working with TRINAT as his student as well

as for instilling in me a part of his deep love for physics. 1 only wish ive could have

worked together longer because 1 know there was still much more that 1 could have

learned. Thanks to the intervention of Peter Jackson who took over the responsibility

of supervising me, 1 was able to continue my studies. In addition to helping me with

analysis and offering ideas on a daily basis, his comments and suggestions on countless drafts of this thesis have been used throughout and have been an immense belp to

me. John Behr also deserves much credit, for he was the one who first helped me

fumble my way through TRIWAT'S complicated hardware, and was instrumental in

the testing and characterization of the scintillator. He has always played an active

d e in helping me with analysis, performing complementary calculations and taking

the time to talk about physics.

1 would also like to thank my supervisory cornmittee, Byron Jennings, Howard

Trottier and Mike Vetterli for taking an interest in my work and for the help they

have given me.

My fellow TIUNAT grad students have made the day- tday routine mucb more

pleasant, especially on those the long, stressful days before and during runs. 1 owe

a lot to Alexandre Gorelov for his work that is used in this thesis which includes

(but is not limited to): his recoil tracking code for GEANT; the new DSSSD mount;

Figures 3.6, 4.6, (the cube of) 3.4 and B.l; aiso, he has continually helped me with

setting up and optimizing the hardware. 1 have also learned many cornputer and 'shop' skiils from him, but perhaps most importantly, 1 would like to thank him for

always being up for a coffee/smoke break; 1 have valued our conversations together

vii

whether they were about physics, current news, or yes, even the war in the Balkans!

Mike Ttinczek has b e n a great help tù my mental health by always staying positive

and taking the time to chat with me about physics as well as life in general. He

also tried tu foster my physical activity through voiieyball, basketbal1 and succer, but unfortunately, he's only human. As a result of his use of GEANT, a number of bugs

were discovered in the code and fixed, and 1 thank him for useful comments especially

with regard to appendix B-2. Good luck with writing up, guys!

1 would like to thank the following members of the group for being additional

sources of information and guidance. Ulrich Giesen, who set up the hardware for

the DSSSD and is responsible for the basis of TRINAT'S hardware as a whole, always

left his door open and my only regret is 1 didn't use it often enough while he was in

Vancouver. I owe a lot of the clarity in Chapter 2 to Pierre Dubé who was alwvays

interested in my work even though it wasn't atomic physics. 1 have had many useful

discussions with Parker Alford who has also helped editingdrafts of this thesis. 1 \vould

also like to thank Trevor Stocki for Looking the thesis over, especially appendk B.L. 1 clid not get a chance to spend as much time with the Jens' that passed through

the group (Dilling and Schmid), but am happy to have had the pleasure of wvorking

with them. I: would like to extend a special thanks to Jens Dilling for making a special

effort to make me feel welcome at TRIUMF when 1 first joined the group.

Many thanks needs to go to Steve Chan and the rest of the guys in the scintillator

shop. If not for their patient natures, flexibility with rushed orders, and extended

experience with scintiiiators, the one used in this thesis surely tvould not have been made as quickly or with as good a quality.

1 would also like to acknowledge various help and useful cliscussions from John

DYAuria, Guy Savard, Tom Davinson, Ted Clifford, Pierre ,haudruz, Renée Poutis-

sou, Peter Machule and Jimmy Chow. The stabilization of the scbtillator would not

have been possible without the generosity of York Holler who has lent TRINAT two of

his units. Joe Chuma has written an excellent program in physica, which has been

used throughout this thesis. Also, thanks to Anna Gelbart for providing me with the

basis for Figure 3.5.

The graduate secretary, Candida Mazza, has shielded me Erom much of the pa-

p e m r k and ha kept track of important dates for me; thank you for Lettiug me

concentrate on physics rather than worrying about bureaurocratic details. Finaity, 1 would like to thank Jan Blanchard, my family and my friends for their

continued support and for always believing in me. Jan, you have been my best üiend since the McMaster days, and always having you around through the good times and the bad has made living here in Vancouver infinitely easier. Thank you for taking a genuine interest in my work and for keeping my head on my shoulden these last few

years! Mom, babi, L m n and Sonja: there is no way 1 would have been here if not for your love, faith and support - 1 hope I've made you proud!

Table of Contents

Approvai

Abstract

Acknowledgements

Table of Contents

List of Tables

List of Figures

. . 11

iii

vii

X

xiii

xiv

Chapter 1 Introduction 1

Chapter 2 /3 Decay and Fundamental Symrnetries 4

2.1 The Fermi Mode1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 A Generalized Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 10

Chapter 3 The /3 - v Correlation Experiment 14

3.1 Using 38mK to rneasure a . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 Tkapping Techniques . . . . . . . . . . . . . . . . . . . . . . . . - . . . 19

3.2.1 The Neutrd Atom Trap . - . . . . . . . . . . . . . . . . . . . . 19 3.2.2 TRIUMF'S Radioactive Potassium Source . . . . . . . . . . . . . 23

3.2.3 TRINAT'S Double MOT System . . . . . . . . . . . . . . . . . . 26

3.3 Nuclear Detection System . . . . . . . . . . . . . . . . . . . . . . . . . 28

Chapter 4 The Positron Detector 3 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Design and Construction 31

. . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Design Considerations 31 . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 GEANT Simulations 32

. . . . . . . . . . . . . . . . . 4.1.3 The Final Design of the Telescope 37

. . . . . . . . . . . . . . . . . 4.2 The Double Sided Silicon Strip Detector 41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 TheDevice 41

. . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Energy Calibration 43 . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Extended Calibrations 46

. . . . . . . . . . . . . . . . 4.2.4 Characterization of the Resolution 51 . . . . . . . . . . . . . 4.2.5 Position Decoding and Analysis Scheme 56

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 38mK Results 60 . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 The Plastic Scintillator 62

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Optimization 63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Timing 64

. . . . . . . . . . . . . . . . 4.3.3 Energy Calibration and Resolution 66 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Stabilization 74

. . . . . . . . . . . . 4.3.5 38mK Results and an Extended Calibration 78 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 The Ptelescope 86

. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Total p Energy 88 . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Backscattering Losses 93 . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Uniformity of Response 94

. . . . . . . . . . . . . . . . . . . . 4.4.4 The Fierz Interference Term 95 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 @-Ar Coincidences 96

. . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Scattering Efïects 97 . . . . . . . . . . . . . . . . . . . . 4.5.2 Recoil Coincident ,f3 Spectra 102

Chapter 5 Conclusions 106

Appendix A Response function of the scintillator 109 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Saturation Mects 110

TABLE OF CONTENTS xii

A.2 Bremsstrahlung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 A.3 Annihilation Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Appendix B GEANT and Future Work 117 B.1 Future geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 B.2 Massive neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Appendix C Electronics of the bTelescope 122

Bibliography

List of Tables

Possible forms for an interaction consistent with Lorentz invariance . . . 5

. . . . . . . . . . . . . . . . . . . . . ISAC radioactive beam intensities 26

Low-energy photon sources used to provide an initial calibration of the . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . strip detector 44

Fit parameters of the DSSSD stries off-line source calibration . . + . . 47 DSSSD calibration fits of E4i = (E, ) = crri x EXi + Px. . . . . . . . . . 50

. . . . . . . . . DSSSD calibration fits of E;i = (Ex) = ayi x Eyi + Py. 52

. . . . . . . . . . . . . . . . Final midths of the DSSSD energy readings 55

. . . . . . . . . . . . . . . . . y calibration of scintillator for April 1999 71

Map of the X' dependence on the low-energy cut-off of the fitting region 84

. . . . . . . . . . . . . . . . GEANT calculations of ,d scattering effects 100

List of Figures

2.1 Fermi's mode1 for B+ decay . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 General Feynman diagrams for a Of -4 O+ B+ decay . . . . . . . . . . 11

3.1 Nuclear energy levels for 38mK . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Recoil time-of-flight vs . B energy in a back-to-back geometl . . . . . . 16

3.3 Atomic energy levels of 38mK in a l-D MOT . . . . . . . . . . . . . . . 22

3.4 Schematic diagram of a vapour-ce11 MOT and neutralizer . . . . . . . . 24

3.5 The Is~c radioactive beam facility . . . . . . . . . . . . . . . . . . . . 25

3.6 Schematic diagram of TRTNAT'S ,4? - v correlation experirnent . . . . . . 27

3.7 Schematic diagram of an MCP detector . . . . . . . . . . . . . . . . . . 29

4.1 GEANT response functions of a plastic scintillator . . . . . . . . . . . . 33 4.2 MC of events lost due to multiple scattering in the DSSSD . . . . . . . 34

4.3 MC simulations depicting where positrons annihilate in the scintillator . 35 4.4 MC design simulations of multiple scattering effects due to the /3 window 37 4.5 Schematic diagram of the P-telescope assembly . . . . . . . . . . . . . . 38

4.6 Schematic diagram of the DSSSD mounting . . . . . . . . . . . . . . - 39

4.7 Geometry of TRINAT'S detection chamber input into GEANT . . . . . . 40

4.8 Schematic diagram of a p+n double-sided silicon strip detector . . . . . 42

4.9 Sample fits to the DSSSD energy spectrum of *"Am . . . . . . . . . . 45

4.10 Energy calibration of the DSSSD strips x2 and y2 using 133Ba and '"-Am 46

4.11 Comparison of Ex and Ey using the off-line calibrations . . . . . . . . . 50

4.12 Comparison of Ey, and Ey, to the corrected E: . . . . . . . . . . . . . 52

4.13 Plot of E:,, vs . (E;) - E;,, . . . . . . . . . . . . . . . . . . . . . . . . 03

4.14 Resolution hnction for strips xl. x12, y1 and y12 . . . . . . . . . . . . . 54

4.15 Block diagram of the DSSSD analysis scheme . . . . . . . . . . . . . . 56

4.16 PositionofDSSSDB hitsinz . . . . . . . . . . . . . . . . . . . . . . . 59

4.17 Average position of inter-strip DSSSD events . . . . . . . . . . . . . . . 60

4.18 DSSSD energy spectrum of the on-line 38mK . . . . . . . . . . . . . . . 61

4.19 207Bi spectra using different scintiilator wrapping schemes . . . . . . . . 64

4.20 Scintillator-MCP timing . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.21 Kinematics of the Compton effect and the scattered electron's spectrum 67

4.22 Fits of a 88Y Compton spectrum to a GEANT simulation . . . . . . . . 70

4.23 Calibration of May 2nd, 1999 using the Compton edges of y sources . . 73

4.24 Non-linear fit to the scintillator's calibration y sources . . . . . . . . . 73

4.25 Resalution of the scintitlator as determined by fits to Compton edges . 75

4.26 Stabilization test of the scintillator's gain . . . . . . . . . . . . . . . . . 76

4.27 Long term test of the scintillator stabilization system . . . . . . . . . . 77

4.28 Scintillator Kurie plots for different AEDSSSD conditions . . . . . . . . . 80

4.29 Fit of the 38mK spectrum to a MC simulation . . . . . . . . . . . . . . 82

4.30 Fit of the 38mK spectrum above 2.2 MeV to a MC simulation . . . . . . 87

4.31 The telescope's B spectra for different AEDsssD conditions . . . . . . . 89

4.32 Fit of the 38mK Tp spectrum to a MC simulation . . . . . . . . . . . . . 91

4.33 Fit of the 38mK Tp spectrum above 2.3 MeV to a MC simulation . . . . 92

4.34 Uniformity of response of the scintillator . . . . . . . . . . . . . . . . . 95

4.35 MC simulation of the recoii TOF versus B energy for ArfL recoils . . . 98

4-36 Scatter plot of recoil TOF versus Tp from the on-line 38mK . . . . . . - 101

4.37 TOF projections for the ArfL and comparison to GEANT . . . . . . . -101

. . . . . . . 4.38 The 38mK /3 spectra gated on Ap?+1-+2 recoil coincidences 103

4.39 The 38mK P spectrum gated on .Ar f 3 p H recoil coincidence . . . . . . . . 104

A l Total cross-sections for the energy loss of positrons in plastic . . . . . . 111

A.2 MC simulation of saturation effects in plastic . . . . . . . . . . . . . . . 112

A.3 Radiative energy loses in plastic ancl silicon . . . . . . . . . . . . . . . 114

B.1 Schematic diagram of TRINAT'S new electmstatic hoop design . . . . . 118

B.2 Kinematics of 38mK decay with massive neutrinos . . . . . . . . . . . . 120

LIST OF FIGURES xvi

C.1 Electronics diagram for the P-telescope . . , . . . . . . . . . . . . . . . 123

Introduction

As Hawking and other physicists believe (albeit with reservation), we appear to be

very close to finally understanding the fundamental laws governing the universe. Im-

proved technologies have allowed measurements that are testing to greater and greater

precision the current theory of particle physics: the Standard Model. This mode1 is

comprised of quantum electrodynamics (describes electromagnetic processes), the elec-

troweak theory of Glashow, Weinberg and Salam (unifies weak and electrornagnetic

forces) and quantum chromodynarnics (governs strong interactions). The Standard

Model cannot be the 'final theory,' howvever, because i t cloes not unify the electroweak

and strong interactions. A 'Grand Unified Theory' is one in which al1 three interac-

tions are seen to be low-energy manifestations of a single force. The next (and perhaps

final?) step would be to include gravity so that al1 four forces would be described by

one ultimate theory.

Hawking retains "optimi~m'~ that a unified theory wilI one day soon be discovered.

Perhaps it will be; or, Like at the end of the 1800'~~ perhaps it will be that ive will

find evidence of new physics, this time fiom results outside the Standard Model. It

is my "optimistic" hope that this wilI be the case so that the physics community \vil1

have many new questions to answer for a long time to come.

The Standard Model has to date stubbornly resisted any attempts at proving it

wrong; it remaïns one of the most thoroughly tested models in science, and has not

failed yet. It is important to continue searching For physics beyond the Standard

Model because any deviation wodd be an important guide for, or test of, a unified

t heory.

Precision /3 decay experiments can be a sensitive test of the Standard Model be-

CHAPTER 1 INTRODUCTION 2

cause they are inherently weak processes. The novel technology of neutrai atom traps

has opened the door to a new generation of /3 decay experirnents. TRINAT has utilized

this technology and is currentLy rneasuring the B - v correlation parameter, a, in the

0'- O+ ,û+ decay of 38mK. The value of a is a sensitive probe of possible scalar

contributions to the weak interaction; a measurement to 0.1% precision would com-

plement the high-energy searches at accelerators. Although continued data collection

is planned to increase statistics with an improved geometry, TRINAT currently has

enough for a 0.3% measurement.

This thesis, after an overview of the theory and the correlation experiment, will

describe the design and characterization of the 0-telescope used by TRINAT to observe

the momentum of the emitted positron.

Chapter 2 is an introduction to the theory of f l decay. The tint section provides

a detailed description of Fermi's mode1 so that the readet can have an intuitive un-

derstanding of the decay. The more modern and general view of 0 decay is outlined

in the second section, and shows how the correlation parameter affects the decay. A number of books 11, 2, 31 were useù as general reierence guides For this section.

Chapter 3 is rneant to provide details specific to the correlation experiment. Details

of the method TRINAT is using to measure a are given in the first section. Following

this is an overview of magneto-optic traps and how TRINAT uses them in the exper-

iment. The last section gives a brief description of the nuclear detection system as

a whole, which consists of the 0-telescope contained in this thesis as well as a recoil

detector.

Chapter 4 describes in detail the P-telescope. The first section explains how the

the telescope as a whoIe was designeci and with what considerations. Section 2 is a

detaiied description of the double-sided silicon-strip detector, its characteristics and

the results obtained from the 38mK data. Following this is a similar section, this

time dedicated to the plastic scintillator. Section 4 presents on-line results of the

@-telexope as a whole and the final section gives a preliminary analysis of the ,&Ar coincidence spectra, although no attempt is made to calcdate a as it is outside the

CHAPTER 1 INTRODUCTION 3

scope of this thesis.

Chapter 5 is simply a summary of important results and suggestions for future endeavors.

,6 Decay and Fundamental S ymmet ries

,û decay has proven to be an invaluable tool in our study of nuclear

and particle physics since the discovery of radioactive decay at the turn

of the century. Early experiments observed only two decay products: the

recoiling daughter atom and a charge-conserving ',û ray,' which was soon

realized to be either an electron (P') or a positron (O+). The simple

kinematics of such a two-body decay wvould require that the P energy

spectrum be a peak corresponding to the energy released in the transition,

as in a decay. The fact that the emitted P ray was observed to have

a continuous energy spectrum prompted Pauli in 1931 to propose that

fl decay is a 3-body process, the extra product being a light (or even

massless), neutral particle that interacts very weakly with matter and so

escapes detection. Only three years later, but twenty years before it was

ever proven to exist, Fermi called this elusive particle a neutrino when he

incorporated it in his theory of @ decay. Fermi's mode1 provides us with a simple, intuitive understanding of /3 decay that, even to this day, remains

essentially unchanged.

2.1 The Fermi Mode1

A nucleus that undergoes decay converts one of its neutrons into a proton, or vice

versa, so that its nuclear charge, 2, changes by A l but the total number of nucleons,

TABLE 2.1: Possible foms for an interaction consistent with Lorentz invariance.

Type Scdar

Pseudo-scdar

Vector

Axial vector

'rensor

A, remains constant. The basic processes underlying these decays a t the nucteon level

are:

Operator

1

"Is

TP Yp75

?,,ru - 'Yv-Yp

n - + p + e - + F e p-dway

p - n + ef + Y, O+ decay

p + e- --+ n + v, orbital electron capture (E)

i n e n Fermi first proposai his theory [41, little else was known except that the

force inducing the decay was weak compared to the strong force binding the protons

and neutrons together to form the nucleus. This a l l o r d Fermi to use first order

perturbation theory to derive his Golden Rule, which gives the transition rate for any

suitably weak potential v,, (using natural units so that A = c = 1);

where M A = I,+j kt II, d3x is the matrix element of the interaction and p(Ef) is the density of states avaiiable to a final state of energy EI. The mathematical form

of FnL for weak interactions is not predicted by Fermi's theory, but there are only five

combinations of the y-matrices that are Lorentz covariant; these interaction t-vpes are

given in Table 2.1. Inspired by electromagnetism, Fermi guessed a vector form for the

interaction whose strengtht is characterized by a coupling constant, GF. The Feynman

diagram of Figure 2.1 is Fermi's mode1 of the P+ decay of a nucleus, AX, using the

more modern concepts of hadron and lepton currents. The following discussion will be restricted to p+ decay, but calculations for p- decay are the same except for the

direction of the currents.

The contact nature of the mode1 implies the matrix element is simply a contraction

of the two currents:

where the lepton current is simply given by

The hadron current is siightly more complicated because it must transform one

of the protons within the nucleus into a neutron. This involves isospin, a symmetry

of the strong interaction, which views protons and neutrons as two 'states' of the

same particle, the nucleon. The isospin of a nucleon is T = $ and the projectionst

2'3 correspond to the two distinct states, the proton (T3 = -I) 2 and the neutron

(T1 = fi). The SU(2) structure of isospin is the same as angular momentum so

there are ladder operators, r*IT 'ri,) = JT(T + 1) - T3 (T3 f 1) IT T3 1), which

transform between these nucleon states. The hadron current for P+ decay is:

where Ive use the r+ operator since the isospin is raised in $+ decay.

ClVe begin calculation of the hadron current by separating the wavefunction of the

decaying nucleon from that of the remaining nucleus:

and

Here .SI, and $&, represent the isospin components of the initiai and final state (over-

dl) nuclear wavefunctions. Treating the nucleons as stmctureless, Dirac particles, we

use wavefunctions of the fornt

+In partide phpics, the convention is reverseci with the proton in the TS = f i subtevel. t~otlowing the convention of Halzen and Martin [II.

FIGURE 2.1: Fermi's contact, vector-interaction model for the Bf decay f ; ~ - z- 1 AY + ef + ue.

where the x spinors carry the spin of the nucleons. The energy released in P decay is

much smaller than the nucleon masses; thus we can take the non-relativistic limit of

Equations (2.7) and (2.8). The overall nuclear wavefunctions are then:

,@,y - J?E; (O) e - i E p t ,+nucl @, E P - ~

Substituting these expressions in Equation (2.4)' the hadron current in the non-

relativistic limit becomes:

Note that in this limit, only the p = O (time) cornponeut of 7' contributes to the

matrk element. The spatial components, responsible for leaving the neutron in a spin

state difIerent from that of the proton, do not contribute in Fermi's vector model of

,B decay.

The leptons are naturaliy assigned Dirac wavefunctions, but h this case the non-

relativistic reduction is not valid. We only need the time component of the current

as for the hadrons, so the lepton current is

where for the sake of generality Ive do not assume a massless neutrino. fl decay

energies are on the order of a few MeV and typical nuclear sizes are a few femtometers;

therefore, over the nuclear volume, (p , + p,) . x (< 1. This ailows us to expand

the exponential in Equation (2.12) and to keep only the tirst term (the "allowed

approximation1'):

Physically, the allowed term corresponds to the leptons being created at x = O with

no net orbital angular momentum carried away; any change in nuclear spin must be

reflected in the aiignment of the spins of the leptons which can be either parallel

(S = 1) or anti-paratlel (S = O). For the Fermi decays we are considering, the lepton

spins must be anti-parallel since according to Equation (2.11), the hadron current

vanishes if X, $ X, so there can be no net change in the nuclear spin, 1. The lepton

spins can be parallel in B decay, but in this case the operator is axial-vector, which

Fermi did not consider; these are referred to as Gamow-Teller decays which have the

selection d e A i = O, f 1. If I" = Of for both the initial and final nuclei (where

r refers to their parity), A l = O but since no orbital angular momentum can be

transferred, it must be a 'pure Fermi' decay (no Gamow-Teller components).

The matriv element, Equation (2.2), of Fermi's fl+ decay c m now be evpressed

as:

where k/[F is the (Fermi) nvclear matrix element of this decay which accounts for the

effects of nuclear structure. Our choice of wavefunction normalization corresponds

to having 2E particies per unit volume, that is uh = vtv = 2E, which we use after

quaring the matrix element Equation (2.14):

This choice of normalization also makes calculating the density of states rather

simple: with 2E particles, the individual phase space available to a particle in the

momentum element p+d3p is simply (d3p/(2?r)3)/2E. On the basis of Equation (2.1)'

the differential decay rate of ZX 3 '-:Y + e+ + u. from rest is

with energy-rnomentum conservation ensured through the 64 function. The matrix

element contains the 'physics' of the interaction, but the observed spectrum shape

will be dominated by the final state phase space. Letting Eo represent the energy

released in the decay, substituting Equation (2.15) into Equation (2.16), and using

the relation p2dp = p 2 f d ~ for both the electron and the neutrino gives

Finally, we use the 6 function to integrate over dE, so that ive end up with the

decay rate:

The additional 'Fermi factor', F(Ee,Zt,R), accounts for Coulomb interactions between the emitted positron and daughter nucleus. Fermi derived an analytic expres-

sion For this function when he b t proposed his theory 161:

where s = d m l 11 = *Ee/pe and Ris the nuclear radius taken to be 1.2 A ' / ~ fm. cr = e2/47r is the fine structure constant and 2' refers to the daughter nucleus. Due

to the difficulty of evaluating the complex I' function, Fermi used a non-relativistic

approximation but since we now have cornputers to aid us, Equation 2.19 is used in

calculations throughout t his t hesis.

Althougb Fermi's theory worked very well, there were still problems (specifically

with the decay of the kaon system) which prompted Lee and Yang [71 to question

whether parity was strictly conserved as required by a purely vector coupling, There

were, after ail, four other types of interactions (Table 2.1) which Fermi could choose

from, and some do not conserve parity. Madame Wu's experiments with polarized

60Co, as well as more accurate experiments that followed, indicate that parity is

mmirnally violated in weak interactions. The form of the weak operator as presently understood is V - A; it is the (equally large) axial-vector component which aIlows

Gamow-Teller decays.

2.2 A Generalized Interaction

Modern particle physics is based on quantum field theory in which the forces are

mediated by the exchange of particles, the quanta of the fielcl. The electromagnetic

force, for example, is mediated by the emission and absorption of its quantiaed fieid, the photon. For the weak force, there are three massive bosons: the W* which carry

one unit of electric charge and the Z0 which mediates weak neutral currents. The

weak coupling constant, g,, is related to Fermi's constant by

and gives the relative strength of the mak force. The mass of the W* has been mea-

sured (5) to be 80.41 f 0.10 GeV so that g, x 0.653 is greater than the corresponding

constant for the electromagnetic force, g, = 6 x 0.303. Indeed, the only reason

this force is 'weak' compared to that of electromagnetism is because of the large mass

of the propagator-

If we limit ourselves to pure Fermi decays (ones where there are no Gamow-Teller

components in the matrix element), then the axial vector component of the weak

interaction vanishes as mentioned earlier. SMilariy? the pseudo-scalar and tensor

components do not contribute. Consequently, we oniy have to consider vector and

scalar interactions; with only Lorentz invariance required, Figure 2.2 shows their

Feynman diagrams. The strength of each interaction type is reflected in the lepton

vertex parameters, CSpv and C&,V, which must be determined experimentally. The S

stands for a scalar current and the V for vector; the primed parameters allow for parity non-conservation in the lepton current, while tirne-reversal invariance is assured oniy

if al1 the parameters are real. We furthermore assume for simplicity that the scalar coupling constant is the sarne as the vector, and that the scalar boson's m a s is the

same as the charged W . In the limit that the momentum transfer, k, is small compared to the LV mass

(applicable to /3 decay), the propagaton reduce to constants: (vector) and 4 (scalar). It is for this reason that Fermi's contact approximation worked so well:

the mass of the W makes the interaction extremely short-ranged (on the order of

l/MI.v x 0.003 fm). The interactions depicted in the diagrams of Figure 2.2 are (with the same limits/approximations as in 52.1):

-i(gpu-k&/M$) (a) vector propagator: kl-hffv (b) scalar propagator:

FIGURE 2.2: General Feynman diagrams for the OC+ Of P+ decay of 5.X - ' - ;~+e++v. as mediated by a massive boson. The expressions for the propagators are given below for bath vector and scalar interactions.

Note that in the non-relativistic b i t , the hadron current is the same for vector

interactions as it is for scalar. The final matrix element is Mli = Mv +Ms which, after squaring and evaluating

the traces, yields three terms:

Ee EvC P e Pv.

IMrI2= 1 6 ~ p M W v ~ G [ ( I c s ~ + I c ~ I ~ ) (1 - =) -

M ~ M ~ + M ~ M , = ~GE,,E,,E.E,G~

-el (2.2,) 2%e(CvCS + C' Ch -

Insertion of these equations into Equation (2.16) and continuing the same calculation

yields the generalization of (2.18), the decay rate for vector and/or scalar interactions

where massive bosons propagate the force:

The decay rate of Fermi's mode1 is effectively renormalized by

and the other parameters are defined as:

in the Standard Model, Cs = CL = O and Cv = CL so that for O++ O+ decays,

it predicts that the p- v correlation parameter a = 1. If instead the weak interaction

is mediated by a scalar boson (Le. Cs = CS and Cv = C(I = O), then the correlation

parameter is equal to -1; in this manner, a precise measurement of a provides a very

sensitive test of possible scalar currents in weak interactions. A determination of a to

nrithin f0.5% would be complementary to more direct high-energy searches [8, 91. The

best meanirement to date is of 6 = i+4(:e,g) = 0.9989 f 0.0052 sys f 0.0039 sys [101 from a detailed measurement of the energy spectrum of P delayed protons from the

pure Fermi decay of 32Ar(Of, T = 2) to the lowest O f , T = 2 excited state of 32Cl.

The b, and 6, parameters are the amplitudes of the Fierz interference terms which

uise from the M ~ M S + MLMV cross terms in the matrù element; beU represents

an interference between the electron and neutrino wavefunctions within each of the

vector and scalar interactions. The bue and b,, terms are negligibly small (indeed,

possibly zero) since m, « Eue, but are included for completeness and to expose the

symmetry. A limit of IbelS 0.007 has been independently placed using measurements

of the Ft values of Of -4 Of decays [Ill. Jackson, Trieman and Wyld [121 were the first to calculate the general decay rate

Equation (2.24) for allowved ,8-decays (including mixed Fermi/Gamow-Teller transi-

tions). Their calcuIations assume a massless neutrino and so do not include the 6, and bew terms. They do, however, include Coulomb corrections [131 which adds a

LZm%%(CsC; PC +CkCg)/ [ICs12+(C~12+l~v12+IC~12] term to a and multiplies b. by

the relativistic factor d m .

The ,tl - v Correlation Experiment

The of decay of the isomeric state of potassium-38 is one of the a g

proximately twenty known cases of strong O++ O+ decays that Nature

has ofTered us and, as an alkali atom, is perfectly suited for neutral atom

traps. The decay 38mK -+" B + ee+ + ut from a trap provides us with

an excellent laboratory with which to search for scalar currents.

This chapter is rneaat to provide some details specific to TRINAT'S 0-v correlation experiment . The first section explains how the observables of

the decay in the back-t+back geometry can be used to determine a. Fol- loiving this is a brief introduction to neutral atom traps, TRIN.W'S double-

trap system and how ive get our radioactive potassium. An overview of

our detection system as a whole is given in the Cinal section which pri-

marily deds with the recoil detector since the P-telescope is the focus of

Chapter 4.

The decay schemes for both the isomer and ground state ildl are given in Figure 3.1.

The 38mK decay is a pure Fermi transition with a branching ratio measured 1151 to

be > 99.998% and a Q-valuet of 5.02234(12) MeV [16l. The 3BK decay is also given

because I s~c ' s mass analyzer (see 53.2.2) canot isomerically differentiate between

the ground state and 38mK, making us susceptible to the ground state7s .y background.

In what follows, let us consider observing the decay fiom a point-like source in

tFor /3+ decay, Q = E, - me.

3.1 USING ""K TO MEASURE a 15

3 8 m ~ ) = 5.02234(12) MeV QP+ (19 E, = 130.4 keV

F~CURE 3.1: Nuciear (log f t = 3.5) is by far pf decay feeds the Zf

energy ievels for 38mK. The superallowed Pf decay the most favoured branch for the isorner. The ground state's state resdting in a 2.17 MeV y.

the back-to-back geometry where the positron is emitted opposite the recoil. The

neutrino may be emitted either (a) pardel to the P or (b) parallel to the recoil. The

kinematics of the decay will be different for the two cases as shown in Figure 3.2; this

is a plot of the recoii's tirneof-flight (T'OF) against the positron's (kinetic) energy.

The recoil TOF is the observable used in the correlation experiment (along with

the position of the event) to determine the recoil momentum, so we use the TOF here for consistency. The TOF is uearly independent of P energy in the fast branch

(case (a)) because the recoil velocity is not seriously affected by how the leptons

share the rest of the available energy: the recoil velocity is [E, - Ee(l - ve)] /MAr,

which is a constant to order (1 - -u,). In the slow branch (case (b)), it is the recoil

which is sharing momentum with the neutrino, and in this case the kinematics yield

v~~ = [Ee(l + ve) - Eo] /hlh. The 0's energy in the asymptotic limit of the slow

branch is defined by the relation: Te + pe = Q. The generalized decay rate, Equation (2.24), shows how the population of the trvo

branches depends on the form of the weak propagator: if purely vector (as in the

FIGURE 3.2: Recoil timeof-ûight vs. B energy for Aro in the back-to-back geometry. For this discussion, we take the neutrino to always be left-handed with helicity = -1 as shown and, depending on the interaction type, the positron is preferentiaiiy emitted with either equal (scdar) or opposite (vector) helicity. The slow and fast branches are either enhanceci or suppressed since the total lepton spin must add up to zero.

6

T 5 - a u

2 4 - M .d

3 - I

'H O l 2 - a, E G 1 -

1 l I l

Vector - (nrpprmstad by ( 1 -

-

-

- "Fast" branch

C

=Ar -. *e+ -. - ."*

*e+ -4

Vector Scalar (mhanced by ( 1 - v&J) ( ~ p p t e s s a d by (1 - Y/=))

3.1 USING 38MK TO MEASURE a 17

Standard Model), a = +l so that the fast branch (je IJ, = cos 88, = 1) is enhancedt

by 1 +v, 2, whereas scalar interactions (a = -1) are suppressedt by 1 - ve 2 0. In the slow branch, cos Op, = -1 so the situation is reversed, and this time it is the

scalar currents which are enhanced (with the vector suppressed). In this way, the

back-to-back geometry is the most sensitive geometry with which to search for weak

scalar bosons.

The enhancement and suppression of the two branches c m be understood physi-

cally in terms of the outgoing lepton helicities. Helicity is defined as the projection of

a particle's spin, E, dong its direction of motion. The projection operators, i(1 j$),

can be used to pick out a particle's helicity, i.e. for the (presently assumed massless)

neutrino, we can project out its left- and right-handed components:

These chiral states are helicity eigenstates with eigenvalues +1 (right) or -1 (left).

For particles with mass, however, this is only true in the relativistic limit since 1171,

where $+ represents a particle (u) and $L an anti-particle (v). Note that for rnmless

particles only, helicity and handedness can be used interchangeably; a left-handed

neutrino will always have negative helicity. A left-handed massive particle on the

other hand predominantly carries negative helicity, but a component that goes like

(1 - E) in the relativistic limit has the 'wrong' (positive) helicity.

To see how this affects the 3smK decay, Iet us for the sake of clarity take the

neutrino to be only left-handed so that the scalar current of Figure 2.2 (on page 11)

then becomes 3v ," (cS + CSy5)ve. The 7= of t he projection operator anti-cornmutes

with the 7' in the adjoint, so zL = ~ i ( l +y) and the current can be seen to only

+Neglecting the negiigible (but conceivably possible) contribution Eiom the b., term.

3.1 USING ""K TO MEASURE U 18

couple left-handed neutrinos to left-handed positrons:

Similarly, right-handed neutrinos only couple to right-handed positrons so that for

scalar interactions, the leptons are emitted with the same handedness. In the limit

of zero mas, their belicities are equal; the positron may have the wrong helicity, but

this is suppressed because it is relativistic and so the approximation in Equation (3.2)

is very good.

The vector current of Figure 2.2 contains a yfi at the vertex, which anti-commutes

with the y5 and so changes the positron projection. A left-handed neutrino in this

case couples only to a right-handed positron (and a right-handed v to a left-handed

ef). Vector interactions, therefore, differ from scalar interactions because the leptons

are emitted with opposite helicities.

As mentioned earlier, the spins of the leptons in a 0'- O' decay must add up to

zero. Retuming to Figure 3.2 (which depicts the lepton spins as fat arrows for each of

the four decay possibilities), it is easy to see how the fast and slow branches are affected

by the type of interaction. In the fast branch, the right-handed positron (resulting

tiom a Standard Mode1 vector boson propagator) naturally has a spin opposite to that

of the neutrino's, and so is allowed. In the scalar case, the dominant spin of the left-

handed positron is aligned with the neutrino's which is forbidden; the positron would

have to have the wrong helicity to be in the fast branch (depicted as the shorter of

the two electron spin arrows). Similarly, the slow branch favours the leptons canying

equal helicity since in this case the neutrino's momentum is opposite the positron's.

TRINAT wiil determine a by simultaneously fitting the recoil TOF spectra for a

number of p energy bins to detailed Monte Carlo simulations. The shape of these

spectra will depend on the ratio of slow to fast branch events and hence a. The B - v

correlation experiment and the anaiysis of its results is largely a part of A. Gorelov's

Ph-D. and so the interested reader is referred to his thesis [la].

3.2 Trapping Techniques

Ever since the first successful experiment where neutral atoms were trapped using

lasers and magnetic fields [191, the use of magneto-optical traps (MOTS) has become

widespread in many fields of physics. The ability to observe radioactive decays from

such traps opens up new possibilities in precision B decay experiments. The MOT

( i ) confines the decays to occur within a compact (= 1 mm3) trap volume, ( i i ) cools

the atoms to temperatures at or below the mK level, and (iii) allows distortion-

free detection of the daughter particles' momenta because of the negligible source

thickness. For this section alone, we use SI units instead of natural units.

3.2.1 The Neutra1 Atom Trap

A unique feature of magneto-optic traps is that their force is dependent upon the

atom's position as well its velocity; much like a spring, the positional force retums

atoms back to a common centre while the latter adds a damping effect, as if the spring

was submerged in a viscous liquid. A laser field generates the velocity-dependent

force which cools the atoms in an optical molasses, while a polarized laser field and

an applied magnetic field adds the positional dependence needed to actually confine

them.

InitiaMy, if one considers how small the incident photon's rnomenturn, hk, is com-

pared to that of thermal atoms, a trap based on the light forces From a laser beam

seems futile. For example, the SII2 4 P3/? (4) transition in 38mK bas a wavelength

of X = 766.5 nm so that Pphor 1.5 eV/c while the atom's thermal momentum is

typically 45 keV/c. In addition, when the atom decays from the excited state via

stimulated emission, this small momentum kick is nullified since the atom will recoil

by -hk if the photon is emitted coherently. Spontaneous emission, on the other hand,

emits photons homogeneously into 47r so that, at least on average, there will be a net

momentum transfer in the direction of the incident photon. Clearly, the atoms must

absorb and spontaneously emit many photons if one hopes to optically trap them. atoms are well-suited for neutral atom traps because they have a simple

electronic configuration; the nsL valence electron alone determines the âne and hyper-

fine structures of the atom since al1 other electrons are in closed (noble gas) shells.

The atomic angular momentum, J = S + L, and nuclear spin, 1, of an atom are a

coupled system, so the good quantum states are IF, mF) where F = J + I. The tran-

sition h m the F = 1 + 4 ground (Si/2) state to the FI = I + excited (P3p) state

cannot decay back into the other F = I - $ ground state since the photon carcies one

unit of angular momentum; the atom must retum to the same F = I + !j ground state

where it started. This 'cycling transition' allows an atom to absorb many photons

from the same laser beam so that the light forces can build up and significantly affect

the atom's motion. The cycling is not perfect due to off-resonant transitions and finite

linewidths, and so atoms rnay be optically pumped into the F = I - state where

they will no longer be in resonance with the laser light. Atorns in this Ldark' state are

not trapped, so to transfer tliem back into the cycling transition, a 'repurnping' laser

is tuned to the F = I - 4 -, F = I + & transition.

It is worth noting at this time that for 38mK, I = O which simplifies the atomic

energy levels; there is no hyperfine structure in an atom with no nuclear spin. In this

case, there is no need for the repumping laser.

Doppler Cooling

Consider the effect on an alkali atom that is placed within a laser field generated

by two identical, counter-propagating laser bearns detuned A MHz below the atornic

resonance, WA. Thermal atoms will have a Mawellian velocity distribution in al1

directions and, due to the Doppler effect, will be affected by each beam differently.

An atom moving collinear with one of the laser beams d l see the light red-shifted

farther below resonance by a factor uatom/c while the counter-propagating beam will

be blue-shifted closer to resonance. The atom wiil preferentially absorb photons

from the laser beam that is against the atom's direction of motion and, with each

absorption, the atom's momentum is reduced. It is in this way that the atorns are

cooled. It can be shown [201 that the force in an opticai molasses is proportionai to the

velocity if ( i ) the Doppler shift isn't too large and (ii) the laser intensity, IL, isn't

strong enough to induce stimulated emission. Letting w t = U A - A represent the

frequency of the laser light, the Doppler force is:

where I' = 1/r is the transition linewidth and I, = " is the saturation intensity.

The transition linewidth ends up being this force's limiting factor; in a simple

mode1 [201, the coldest temperature attainable is TD = hï/2ks where kg is Boltz-

mann's constant. In the case of 38mK for which T = 26 as, this 'Doppler limit' is

150 pK.

The MagnetwOptic Trap

An atom with magnetic moment p subject to a magnetic field, B, will remove the

r n ~ degeneracy and Zeeman split the 1 F, .mF) energy levels according to

where g~ is the (atomic) Landé g-factor and p~ = eh/2m, is the Bohr magneton. If we

apply a linear magnetic field, Bz = Boz, to atoms in an optical molasses (Figure 3.3

depicts this for the 1-D case), the Zeeman effect will provide us with a position-

dependent force: the energy level shifts (hence the transition frequency and scattering

rate) will be proportional to the distance from z = O. An atom at z > O d l have

its 1; 1) - 1 9) transition shifted closer to the laser frequency. The two counter- propagating beams are distinguished by their polarizations; the AmF = -1 transition

can only be driven by the a- beam, so the atom feels a net force acting towards the

left. Similarly, atoms at L < O will preferentially absorb the a+ light through the

I$ +)- 1; 1) transition and be pushed back towards centre. If the laser field does

not have perfect polarization, the atom can absorb photons from the wrong beam and

will be heated rather than cooled. Thus, the quality of the circular polarization of

the laser light is very important.

The magneto-optic force is a combination of the Doppler force with effects induced

by the Zeeman shift. The trap centre is defineci at t = O where the magnetic field

changes sign. If we let = h + ,8t where Pr represents the Zeeman effect on the

(a) z, B c O (b) Z = B = O (c) z. B > O

h h 4 4 \ $ 1 1 \ \ l 1 \ 1 I l II 1 \

1 \ A l \ l \ 1 \ l \ l \ I $ 1

\ 1 \ 1 \ 1 \ 1 A& \ l A m~ = -L 1

2 2 Force no net Force - force f-

FIGURE 3.3: Atomic energy levels and Zeeman shifts of 38mK in a one dimensional magneteoptic trap. The shift of the energy levels depends linearly on the magnetic field (for weak fields) giving a positional dependent force. The trapping arises because of preferential scattering off the laser that is shifted closer to resonance, depicted by the solid Iines arising from a+ light in (a) and a- in (c); the force in either case pushes atoms towards 2 =O. Both laser beams are equdy off resonant at the trap centre (b) so neither is preferentiaily absorbed and the atom feels no net force.

transition frequency, then the overall magneto-optic force is [211

It can be shown that (221, for small detunings, this force is proportional to so that

the trapped atorns behave like a simple, damped harmonic oscillator.

The generalization to three dimensions requires a quadrupole magnetic field that

is zero at the centre and from there, increases linearly with distance; this is generally

accomplished using two coils in the anti-Helmholtz configuration. With six laser

beams oriented along the axes as depicted in Figure 3.4, the forces in the ID case are

present no matter which direction an atom in the trapping volume is travelling. Typically, MOTS are not very deep and so considerable effort is needed to effi-

ciently load them. The rnost popular rnethod is known as the vapour-ce11 MOT [191

and it uses the fact that a MOT can capture the low-energy tail of the Maxwell-

Boltzmann distribution of velocities, The ce11 which defines the trapping volume can

be specially coated (231 so that atoms tend to bounce off the wall rather than (perma-

nently) chemisorbing to it. When they bounce (physisorb), the atoms ce-thermalize

(repopulating the whole ;Llauwell-Boltzmann distribution) and are able to be trapped

by the MOT again. The many repeated opportunities for capture allow this method

of loading the MOT to have efficiencies on the order of several percent.

3.2.2 T R ~ F ' S Radioactive Potassium Source

TRIUMF bas long been interested in developing radioactive ion beams (RIBs) because they offer the ability to study nuclei atvay from the valley of stability. The copious

production of exotic nuclei delivered with low kinetic energy has already been used

by TRINAT as well as an experiment measuring the transition probabilities of su-

perallowed decays which will test the conserved vector current hypothesis [241; future

planned experiments at T R I ~ F ' S RIB Rclude magnetic moment measurements using

the Low Temperature Nuclear Orientation facility [251 as weU as studies using a po-

larized 'Li beam [261. b1edium-energy (0.15-1.5 MeV/u; A<30) EUBs are important

for nuclear astrophysics because theoretical calculations of stellar processes require

measurements of certain nuclear crosssections that affect key steiiar cycles [27, 28).

FIGURE 3.4: Schematic diagram of a vapour-ce11 MOT with an ion beam catcher and neutraiizer. SAC provides us with a potassium ion beam which is neutraiized in the hot Zr cone. The atoms then diffuse out into the vapour-celi MOT and the ones in the low-energy t d of the velocity distribution are able to be trapped in the MOT. The quartz cube defines the trapping volume and is coated with SC-77 Dryfilm [231 so as to maximize the number of bounces off the w d s and increase the trapping efficiency.

FIGURE 3.5: The ISAC radioactive beam facility at TRIULIF. The 500 MeV positrons bombard a Ca0 target, producing a variety of isotopes; a potassium beam is extracted and filtered through a mass spectrometer before being transported to the TRINAT laboratory.

A test facility, TISOL 129, 301, based on the ISOL facility at CERN-ISOLDE (311

has been operational since 1987 to provide low energy RIBs as tell as to develop

a robust target-ion source. The 200 - 500 MeV protons from TRIULIF'S high inten-

sity (150 PA) cyclotron provide an excellent production beam with which to bom-

bard thick targets, and TISOL has proven that a wide variety of radioactive nuclei

can be efficiently produced (500 MeV protons; 1 pA current). Ion beams were

extracted from the target at 6 - 12 keV, and transported to a magnetic andyzer

(mas resolution M/AM = 1600) that had a bend angle of 90" to provide a clean,

tunable beam of radioactive isotopes to the experimental area. TRINAT was able to

successfuily couple TISOL'S RIB to a MOT, continuously trapping 2 000 atoms of 3TK (tLI2 = 1.23 s) and 5000 of 38mK. From this, the viability of the correlation experi-

ment was proven and measurements were made of the isotope shifts [321 in potassium

as well as charge-state distributions of daughter atoms in ,û decay [33, 341. The success of TISOL and the experience gained in developing it has enabled

Isotope Intensity

38mK 2 x 107 ions/sec

38K (bkgd) 5 x 10' ions/sec

TABLE 3.1: [SAC radioactive beam intensities.

TRIUMF to successfully build a large scale radioactive beam facility: ISAC (the Isotope

Separator and ACcelerator). A schematic diagram of the new beam facility is given in

Figure 3.5. The general idea is the same as for TISOL, but the new surface ion source

can handle more intense production beams (1 pA in June, 1999; currently 10 pA and

up to 100 pA in the future) and the ions cm be extracted between 12-60 keV. ISAC'S mass analyzer consists of a low-resolution pre-separator followed by the former Chalk

River mass separator 1351 which has a mass resolution of 1 5000. The isotopically

selected RIB is then transported to the various experimental areas; in the case of TRINAT, the beam is deposited into a conical zirconium foi1 as indicated in Figure 3.4.

ISAC'S first radioactive beams, 37*38mK, were produced on November 30, 1998. By

TRINAT'S June 1999 run, ISAC had already demonstrated the ability to produce these

beams with intensities comparable to those attained at TISOL (see Table 3.1). The vapour-ce11 MOT of Figure 3.4 aiiows an efficient loading of atoms into the trap, but

is completely incompatible with obseMng the recoil of the decays. Efficient loading

of an open MOT can be obtained by carefully transporting atoms already trapped in

the vapour-ce11 MOT; this system is outhed in the next section.

3.2.3 TRINAT'S Double MOT System

in order to reduce backgrounds as well as to isomerically differentiate between 38K and 38mK, a double-MOT system is utilized (see Figure 3.6). The first 'collection

trap' is a vapour-cell MOT that traps the potassium atoms once they diffuse out of

the hot Zr neutraiizer (which is based on the Los Alamos scheme [361). The laser

linewidth is small enough to resolve the difiecent fine structure of the isomer and

ground state, so only the isomer is trapped. The cold, trapped 38mK atoms at the

centre of the collection trap are then pushed with a smali (w 1 d) pulsed Iaser

FIGURE 3.6: Schematic diagram of TRINAT'S B - u correlation experiment. The ion beam from ISAC is deposited and neutralized in a Zr foi1 and then trapped in the first 'collection' trap. The cold, trapped atoms are then transferred to the 2" trap where the decay is observed using a micro-channel plate (recoils) and the Ptelescope (positrons).

beam to a second 'detection trap.' The push beam, airned a few millimeters above

the 2" MOT so as not to interfere with any atorns already trapped there, generates

a low-energy (vat,, 40 m/s) atomic beam of 38mK that can be directly captured in

the detection trap. The large separation of the two traps reduces the probability of

a thermal 38K randody entering the detection charnber, and so provides a cleaner

environment from which to observe the decay.

As the atoms are being transferred they expand radially, so the efficiency of the

transfer wiil rapidly decrease as the inter-trap distance is increased. In order to be

able to separate the detection trap 75 cm (enough to add approximately 15 cm of

lead shielding) without a great loss of atoms, two 2D MOTS ('atomic Funnels') have

been employed t o compress them back dong the push beam axis. The detection trap

typically catches 75% of the atoms pushed from the lSt trap. The efficiency of the

system as a whole, including capture and transfer, is 5 x 104 atoms trapped per ion

incident h t o the neutrdier.

For a more thorough review of TRINAT'S double-MOT system and the details

regarding the transfer, the interested reader is referred to [371.

3.3 Nuclear Detection System

The P - v correlation experiment requires the detection of the recoiling Ar atom and

the emitted P+ and, as rnentioned earlier, is most sensitive to scalar contributions in

the back-to-back geometry. The recoil detector has a nominal active area of 2.6 cm in

diameter and is placed -6.28 cm along the 2 direction from the center of the chamber

(which roughly corresponds to the detection trap center). The ,L-telescope is on the

opposite side and consists of a 1.2 x 1.2 cm2 double-sided silicon strip (AE) detector

at z = +6.76 cm backed by a large plastic scintillator (E) detector. The solid angle

subtended by the recoil and ,L detectors are 0.14 and 0.13 sr respectively.

The MCP purchased from Galileo [381 and depicted in Figure 3.7(a) is a thin array of tens of thousands of tiny cylindrical lead glass channels (10 - 15 Fm in diameter).

Each of the specially formulated micro-channels acts as a miniature electron muiti-

plier tube. An ion incident on one of the channels will generate secondary electrons

which are accelerated down the channel wall and generate further secondary electrons, resulting in a cascade which yields amplifications up to a few times IO4. The applied

high voltage bias provides the electric field along the length of the channel, and s u p

plies the electrons needed for the avalanche. The channels are oriented N 11" with

respect to normal of the MCP surface in arder to minimize variations in the detector's

efficiency as a function of the incident particle's direction which is related to Op-,.

TRINAT'S recoil detector is a combination of three 600 pm thick MCPs in the 2-stack

configuration (see Figure 3.7(b)) with an inter-plate separation of 150 Pm. The signal

from the 2-stack, which has an amplification up to IO", is registered by a resistive

anode which has four separate readouts; the relative distribution of charge between

the readouts allows the position of the recoil to be determined to f0.25 mm.

As T R ~ A T is determinhg the recoil momentum from the position of the hit in the

MCP and its the-of-flight relative to the plastic scintillator, the MCP is operated at

saturation (w 1 keV bias/plate) to make its efficiency as insensitive to the incident

ion's energy as possible. The timing resolution of the MCP is excellent (characteris-

tically hundreds of picoseconds), and so it is not surprishg that the relative timing

between the recoil and ,L detectors is limited by the scintillator's timing (see 8i1.3.2).

The MCP efficiency for Ar recoils can have a strong dependence on the atom's

(a) A micro-channel plate (b) Operation in the 2-stack configuration

FIGURE 3.7: Schematic diagram of an MCP detector and the arrangement used by TRINAT. The distribution of charge of the four resistive anode readouts is used to determine where the event occured.

energy; over energies of O -450 eV, the MCP efficiency is not known. This fact makes

using the neutral Ar recoils for the correlation experiment very difficult because the

slow branch covers a large recoil energy range. For decays where the daughter Ar

is a positive ion, however, this source of systematic error can be greatly reduced;

TRINAT uses a uniform electric field to accelerate the charged Ar recoils up to energies

where the I\1CPts efficiency is known [391 to be relatively Bat SE^[^^ < 2% between

EAr = 5.3 - 5.6 keV).

Additionally, this field separates the different charge states in TOF and increases

the number of detected recoils by focusing Ar ions that wouid have othemise missed

the MCP. Collection of the complete angular distribution is obtained for charge states

greater than +3 with our present field of -829 V/cm.

The double-sided silicon-strip detector (DSSSD) provides both position informa-

tion of the ,8 as well as a coincidence condition to be used with the scintillator to

d u c e background (non+) events. The energy deposited in the scintillator (and, to a

lesser extend, in the DSSSD) together with the position of the hit in the DSSSD pr+

vides us with a measurement of the p's momentum. Therefore, the energy resolution

of the scintillator needs to be as good as possible for the ,8+ momentum reading. With

the recoii and positron's momenta both measured event-by-event, the momentum of

the neutrino can be deduced; in fact the kinematics of the decay are overdetermined, and so we are able to check systematic errors in our experiment.

The Positron Detector

This chapter will first go through the design of the scintillator and will

then go on to the characterization of the A E and the E detectors. The &telescope as a whole is discussed in the h a 1 section where results from

the April/May 1999 run pertinent to the - u correlation experiment will

be presented.

4.1 Design and Construction

For the 0-v correlation experiment to succeed, the emitted positron must be detected with good energy resolution and have good timing relative to the recoil MCP detector.

In general, the energy of P-particles is difficult to measure accurately because they

are relativistic over the 1 - 5 MeV region of interest; because of their small mass,

they scatter easily, into large angles and emit bremsstrahlung radiation which may

escape detection. The situation is worse for Of's since one must also contend with

the possible detection of the annihilation radiation. An added complication is the

possibility of annihilation-in-flight, in which case E, > me and it rnay add to the

low-energy t ail.

4.1.1 Design Considerations

Early T ~ A T expeciments utilized a double-Si(Li) detector in conjunction with a

double-sided Si-strip detector (DSSSD) to fom the E and AE detectors of a 0- telescope, which has been discussed in detail elsewhere [401. The Si(Li) semiconductor

devices naturally have evcellent energy resolution (FWHh,I = 60 - 120 keV over the

4.1 DESIGN AND CONSTRUCTION 32

region of interest) as well as iinear energy responses, but suffer from a number of

serious drawbacks: they have a large low-energy tail from bremsstrahlung and the

large probability of backscattering off the high-2 material; a systematic error for p's

that penetrate the first Si(Li) due to the necessary dead-layer between the detectors;

and its overall change in response (the peak of the response function at 2.5 MeV

is N 3x larger than at 5 MeV) 1401. Simulations of the correlation experiment 1411

compared B-telescopes where the E detector was (1) a double-Si(Li), (2) a 0 4 cm x

4 cm plastic scintillator, (3) a 07.5 cm x 5.1 cm plastic scintillator, and (4) a perfect

detector (6-function response). The simulations used measured response functions from [401 for (1) and (2); the pararnetrized responses of Clifford et. ai's telescope have

been published [42, 431 and were used for (3). The results indicated better sensitivity

to the correlation parameter if a plastic scintillator similar to the Clifford design ivas

used instead of the Si(Li).

4.1.2 GEANT Simulations

In order to optimize the plastic scintillator for TRINAT'S B - v experiment, Monte

Carlo simulations were performed for various geometries using the GEANT detector

description and simulation toot (441. The goal was to design a scintillator that is

insensitive to the entrance angle/position of the 0s upon the DSSSD.

The initiai geometry was extremely simple: a piece of silicon, representing the

DSSSD, was placed in front of a cylindrical scintillator, both 'magically' suspended

in space. The sizes of scintillator considered ranged fiom 4 - 6.5 cm in diameter

and lengths between 3.5 - 6 cm, while the strip detector was constrained to be

2.4 cm x 2.4 cm x 491 pm (the size of the existing detector). The simulations helped

to determine the best compromise between:

1. Too large a scintillator - Compton scattering of the annihilation radiation

adds a high-energy tail (the 'Compton toe') tbat approximately scales with the

volume of the detector.

2. Too small a scintiilator - the positrons may escape the detector before annihi-

lating thereby adding to the low-energy tail; also the likelihood of bremsstrah-

lung radiation escaping increases.


O NO0 2000 3000 4000 5000 6000 Tri. (dashed) or Tc (solid) [keV]

FIGURE 4.1: GEANT simulations of response functions for a 06.5 cm x 5.5 cm plastic scintillator for 1,2,. . . ,5 hieV positrons. The solid line has a resolution Eunction folded in and the DSSSD's energy added back in, while the rlaslird Line represents a perfect energy reading which requires a DSSSD coincidence, but the energy is not added to the scintiiiator's-

Simulations of response functions for a plastic scintillator are depicted in Figure 4.1

for TB = 1,2,. . . , 5 MeV. The high-energy tail is due to Compton summing of the annihilation radiation and is most prominent for 1 MeV positrons (5A.3). The low-

energy tail contains events where the positrons escaped the detector before stopping, but also adding to this tail are cases where bremsstrahlung (radiative) energy lasses

escape the detector (sA.2) and/or the positron annihilates before depositing al1 of its

kinetic energy and the y quanta escape (5A.3).

The optimal geometry

Figure 4.2 shows the percentage of positrons that fired the AE detector but, due to

multiple scattering, missed the scintiliator and therefore represent lost events. The

plot on the leFt has the AE placed 1.0 cm in Front of the E detector while the plot

on the right is the case where it is only 0.3 cm away. The effects of backscattering


+ backscatter off DSSSD

FIGURE 4.2: Monte Carlo design simulation of the fraction of positrons that mdti- ply scattered in the DSSSD and consequently àid not interact with the scintiiiator. The effect depends on the diameter of the scintiiiator if the DSSSD-scintillator spacing is 10 mm (left), but is neariy independent if this spacing is only 3 mm (right). The 7.6 cm x 5.1 cm design, based on Clifford's dimensions [42], was simulated for cornparison.

directly off of the DSSSD is, of course, independent of its position and so the same in both cases. The original DSSSD mount used with the Si(Li) was such that 2.5 cm

was the closest the AE could be to the Front face of the scintillator. The results

of Figure 4.2 indicate that almost al1 of the positrons are fully contained, virtually

regardless of the diameter of the scintillator, if the DSSSD is placed close enough to

the Çont face of the scintillator. This motivated the design and implementation of a

new mount (451 which enabled us to reduce the spacing to 0.292 cm (see also $4.1.3).

A major factor in determinhg the optimal diameter was the requirement that

al1 of the positrons corne to rest and annihilate within the plastic's volume. In the

experiment, the most energetic positrons will have the largest range and so simulations

of 5 MeV positrons were performed Nith a very large scintiiiator to see what the

required length and diameter must be to contain them dl. Figure 4.3(a) shows the


O 1 i s i s f i l a i podUon 01 annihiiatlon [cm]

FIGURE 4.3: Monte Carlo design simulations of a pencil beam of 5 MeV positrons depicting the radius (a) and depth (b) of where in the scintillator the annihiLation occurred. The dashed line in (a) represents the radius of the scintiilator used throughout this thesis.

radius at which the positrons annihilated in the plastic. This aspect of the scintillator

design was based primarily upon this result, but other factors, such as the total

number of accepted events and the relative percentage in the (high- and low-energy)

tails, also supported a larger radius. The dashed line in the figure depicts the final

scintillator's size and one can see that virtually al1 of the positrons are cantained. We would have considered a slightly larger diameter, hoivever mechanicd constraints

due to the existing vacuum chambers limit us to the present design with a 6.5 cm

diameter.

The penetration of the 0s along the length of the scintillator (Figure 4.3(b)) is

weii contained below 2.75 cm. The original analysis scheme for the correlation ex-

perirnent, which involved excluding kinematically forbidden events, was thought to

be very insensitive to the ce-absotption of annihilation radiation, and so any extra

volume was not a major concern. The low-energy tail on the other hand, which was

the instigating factor for switching from the Si(Li) to a plastic, is a potentialiy large

source of systematic error, Therefore, we ordered and (at least for the present t h e )

have continued using a 06.5 cm x 5.5 cm piece of scintillator, saving the option of later cutting the length to = 2.75 cm.

The scintillator used throughout this thesis is 5.5 cm in length, and therefore the

Compton toe of the response function is larger than necessary; dthough we will see


that the present scintillator suffices at this tirne, the existing scintillator should at

some point be compared to one whose depth is only 2.75 cm. If the light collection is

not seriously compromised or if the final analysis scheme does prove to be sensitive

to the re-absorption, the B-telescope should be upgraded with the srnaller piece of

plastic.

The P window

Some of the P-telescope's components (e.g. the scintillator's wrapping) are not com-

patible with the ultra-high vacuum needed by a magneto-optical trap and so it is

housed in a separate ('P-telescope vacuum') chamber as depicted in figure 3.6. The

front face of this chamber is 7 mm thick stainless steel with a 038 mm 'window' the

P particle can enter through to suppress the observation of activity from atoms that

do not decay from the trap. The positrons Coulomb scatter in the foil as they traverse this necessary dead

layer and, if the positron scatters into a large angle, the deduced positron momentum (calculated by the position of the subsequent hit in the DSSSD) would not be cor-

rect. Originally, the p window was a 0.025 mm thick stainless steel foil (2sbt a 26.5);

however, the characteristic scattering angle [461 that defines the cone the ps scatter

into scales with z~'~/$, so the steel is clearly not the optimal material. The scat-

tering angle should be cut in half by using a lower Z material like a commercially

available [47] beryllium foil (type IF1, 2 = 4-14).

In order to see if the position improvements warranted purchashg the relatively

expensive beryllium foil, GEANT simulations were performed to compare the beryllium

(0.127 mm thick) with the stainless steel. Low energy ps have the greater probability

of scattering into large angles, so a pencil beam of 1 MeV positrons was incident

normally on the centre of the P window in the simulations to see the position deviations

caused by the two types of foiis. The geometry in the MC is the same as for the actual

telescope used in the April/May 1999 run, which has the front of the DSSSD 2.9 mm

behind the 0 window. Figure 4.4 shows the radial position of where the positrons hit

the AE after traversing the two types of foiis. The distributions are approximately

Gaussian over the peak (fiom small angle scattering) but have more pronounced tails

arising fiom large angle (Rutherford) scattering. The widths of the distributions are

- Be - -%.Steel

-lo -5 O 5 DSSSD position [mm]

F~CURE 4.4: Monte Carlo design simulations of multiple scattering effects due to the p window. The soiid iine depicts a pencil beam of 1 MeV positrons entering the DSSSD after traversing a 0.127 mm beryllium foil while the tliistictl simulates 0.025 mm stainless steel. Both foils are placed 2.9 mm in front of the DSSSD.

0.46 and 0.97 mm for the beryllium and stainless steel respectively. For the stainless

steel foil, then, a p originally incident towvaràs a given DSSSD strip wvill only have lu

of this distribution firing that strip, whereas 2a will fire the correct one For beryllium.

This factor of two improvement is decidedly worth the effort, and so the ,û window

was changed to the 0.127 mm thick beryllium.

4.1.3 The Final Design of the Telescope

The Telescope Assembly

The realization of the plastic scintillator and of the P-telescope as a whole is depicted

in Figure 4.5. The scintillator, a 06.5 cm x 5.5 cm long BC408 plastic purchased

from Bicron [481, is optically coupled to a plexiglass light guide which in turn is

coupled to a Philips 4312/B 12-stage photomultiplier tube (PMT). Both the plastic

and the light pipe are mapped with a d a s e reflector, Teflon, to increase collection

of the scintillation light as discussed in 84.3.1. The scintillation light produced in

the BC408 (A,, = 425 nm) overlaps the maximum of the bialkali photocathode's

response (400 - 450 nm; 20% quantum efficiency). The Philips PMT was chosen


Date: Mardi 30,1999

FIGURE 4.5: Schematic diagram of the P-telescope assembly (to scalej. The major components are described in the text.

because it was specified to have a good hybrid of energy and timing charactecistics. A transistorized voltage divider assembly (Philips VD123K) was used to minimize gain

fluctuations arising from variations of the dynode voltages.

The /3-telescope's chamber separates the trapping region's 2 x IO-^'' Torr ultra-

high vacuum from the telescope's poorer vacuum of typically 5 x 10-'' Torr. A conflat

fiange was modified by adding two vacuum pumping ports and four 16pin electronic

feedthroughs for the 48 DSSSD strips. The vacuum is maintained by an O-ring which

seals the light guide to the fiange using a specially designed clamp.

The PMT is surrounded by 0.2 mm thick p-metal which, in addition to protecting

the PMT from magnetic fields, also serves to make the system light-tight. A blue

LEDt Mth a nominal wavelength of 450 nm (closely matched to the scintillation

light) is coupled to the PMT Ma a fibre-optic cable as shown in the figure. This is

used to stabilize the PMT gain as discussed in 94.3.4.

The DSSSD is mounted wvithin a plexiglass disk (as shown in figure 4.6) whose

thickness is only slightly larger than the 0.40 cm thick frame of the DSSSD (which

mounts the silicon wafer and houses the strip readout contacts). The low Z matecial and minimal thickness was chosen so as to reduce the probability of 0s scattering

off this mount. The plexiglass plate provides both a rigid muunt as weli as a well-

d e h e d overall DSSSD orientation; with the axes d e b e d in Figures 3.6 and 4.7, the

+A Panasonic digikey #P39û-ND light emitting diode.


FIGURE 4.6: Schematic diagram of the DSSSD mounting showing the strip detector's reference frame relative to that of the detection charnber.

DSSSD is rotated +(45.0 i 0.5)" with the y-strips facing the recoil detector. The

G10 frame represents the largest source of scattered Bs adding to the telescope's low energy tail; as the DSSSD is rnanufactured this way, we are not free to reduce this

contribution mechanicaliy, but we may suppress it in software by not including the

edge strips in the analysis (see 54.2). Coaxial wiring for the strip reaciouts is fed out

of the ,O-telescope's vacuum chamber through the 16-pin feedthroughs, and is input to

locally constructed [491 preamplifiers which are mounted directly on the flange. The

wiring frorn outside the shielded vacuum charnber to the preamplifiers is coaxial (and

additionally are shielded) to prevent noise €rom electrical pick-up.

Final GEANT Geometry

Once the ,O-telescope was built and optimized, a more realistic description of the

geometry vas input in the Monte CarIo simulation. A diagram of t he volumes included

in GEANT is given in Figure 4-7- The ,O window is at z = +6.601 cm and is defined

by the specifications [471 of the IF1 type berybumt. The bulk of DSSSD remains a

pure wafer of silicon, but now the geometry of the detector includes the 48 duminum O

readout strips (assumed to be 500 A thick) and, more importantly with regard to

t99.837% Be, with the biggest contaminations hom Fe (0.006%), Ni (0.02%), Ca (0.02%) and

Zn (0.01%). These percentages, and those hereafter, give the relative number of etements making up the medium.


FIGURE 4.7: Geometry of TRINAT'S detection chamber that is input into further (detailed) Monte Car10 simulations. The volumes outside of the &telescopeYs vacuum charnber are important because positrons cm (back)scatter off of tliem before entering the &telescope.

scattering effects, the G10t frame in which the wafer is rnounted. The plexigiasst

mount was simplified in the MC by apprauimating it as a ring of plastic wbose inner

diameter does not ovedap the GlO frarne. The four stainless steel rods connecting the

DSSSD mount to the (smaller) telescope Range are also included.

The scintillator has 6ve layers of Teflon* on the front face totalling 0.02 cm in

thickness, and many layers around the sides of the scintillator and light guide, totalling

about 0.7 cm in thickness. The BC408 plastic is defined by the hydrogen to carbon

ratio of 1.104, but also contains a 2% addition of PPOtt which is addeci to increase scintillation efficiency 1501. The light guide extends out past the Banges, but other

components behind the flanges (the clamp, the PMT, etc.) were not included because

they will not affect detection of the positron.

The rest of the geornetry inchdes the 2nd trapping charnber, the alurninum hoops

tdefined as 60% Sioz and 40% Kapton (C2HroN205). tdehed as CH2=C(CH3)COzCH3. 'defined as CF2=CF2.

ttdeûned as ClsH~lNtOr (2,5-diphenyloxazole).

for the electric field and the MCP assembly. The material of the MCP plates is

Corning 8161 glassi and the resistive anode is pure Si. A large number of 0's were

found to scatter off the MCP or one of its electrostatic components before entering

the ,O-telescope (see 54.5.1) and so it is important to keep these volumes in the Monte

Carlo, even though it requires w 10x the CPU time. The rods for the hoops, not

included in the simulations presented here, have since been included since they offer

a considerable volume of stainless steel that 0s can scat ter from.

The Double Sided Silicon Strip Detector

This section begins with a brief introduction to these semiconductor devices, but

for a more thorough review, the interesteci reader is referred to 1511. Sections 4.2.2-4 describe the energy calibration and resolution of the detector, followed by the position

decoding scheme in i4.2.5. The final section, $4.2.6, presents the results obtained from the correlation experiment data.

4.2.1 The Device

The AE component of the 0-telescope is a double sided silicon strip detector pur-

chased from Micron Semiconductor 1521. It is a silicon wafer of dimensions 2.4 cm x

2.4 cm x 491 pm upon which a thin (typically a Few pm) p+-type layer is deposited

onto the 'front' or ohmic side of the n-type silicon. Similarly an n'-type layer is

deposited on the grounded side ('rear') of the detector as depicted in Figure 4.8. This O

forms a pf n junction, each side upon which is evaporated a thin (typicaily 500 A) layer of aluminum; a reverse bias of -135 V is applied to the pf side (with the nr side

at ground) to ensure that the depletion layer extends throughout the Si wafer so that

al1 of the energy deposited by an ionizing particle gets coliected onto the duminun

readouts. The negative bias also increases the magnitude of the electric field across

the depletion layer which serves both to make the charge collection more complete as

well as to decrease the time needed for the electrons and holes to reach the readouts

+definecl as 8.8% Pb, 61.1% 0,24.6% Si, 4% K, 0.8% Rb, 0.3%Ba, 0.19%As, 0.08% Cs and 0.15% Na.

FIGURE 4.8: Schematic diagram of a p+n double-sided siiicon strip detector. Electron-hole pairs are created as an ionizing particle goes through the depletion region, and they are separatek collected on readouts on the pi (electrons) and n' (holes) side. Both of these readouts are divided into 24 strips, providing position sensitivity in both 2 and Y.

( i e . the pulse duration). To add position sensitivity ta this detector, the aluminum

readouts are both divided into 24 orthogonal strips whose width and spacing are nom-

inally 900 and 100 pm respectively. The lengths of the pf strips are aligned with I

and so, depending on which strip registers the hole collection, we obtain the position

of the hit in y. Similady, position information in ? is determined by the negative

charge collection on a given n f strip. With a depletion depth of d = 491 Pm, the

capacitance works out to CSkp = A/d = 4.4 pF, where A = 900 pm x 2.4 cm is the

area of a strip.

Upon entering (and exiting) the detector, a charged particle will interact with the

aluminum contacts, thus introducing two necessary (yet entirely negligible) dead lay-

ers. As the particle then goes through the bulk silicon, the energy deposited through

multiple Coulomb scattering in the depletion regiont creates electron-hole pairs; the

tthough fuiiy depleted, the wafer will have smd gaps in its depietion region near the surface of the areas between stnps - carriers generated here do not get coliected with the same efficiency.

positive holes are swept by the electric field to a readout on the ohmic side while

the negative electrons migrate to the readout at ground. Thus for each event, the

DSSSD fires two pulses - one for holes and the other for electrons - which are both

proportional to the energy deposited by the incident particle. The electrons and holes

are created in pairs so the two signals should in fact be identical, although in practice

differences occur due to electronic noise and, hopefully to a lesser extent, uncertainties

in the energy calibration of the strips.

The electronics for the DSSSD is illustrated by the sample strips depicted in the

figure of Appendix C (page 123). The timing of the y-strips is used to trigger events

while the energy signal (of both the x- and y-strips) goes directly to LeCroy 224912

chargôsensitive ADCs. The timing signals are fanned together in groups of four, each of which is then input to the 2228A TDC for separate timing; these six groups

are then fanned together giving any 'DSSSD event' either (a) used to provide an

event trigger (off-line calibrations) or (b) checked to see if it is coincident with the

scintillator's timing (on-line event trigger). The hardware thresholds for each of the

24 triggering strips were individually optimized and set to be above their respective pedestals (5 20 keV).

We will see how with a good energy calibration and an understanding of the detector's resolution, a condition on the difference between the two energy readings

provides a clean tag for /3 events.

4.2.2 Energy Calibration

Low-energy photons from the decay of 241.4m and 13%a were used to calibrate the

strip detector. '33Ba decays by electron capture [531 to a nurnber of excited states in

L33Cs. The resulting radiation consists of Cs X-rays a s well as several y rays, with the

photons of interest listed in Table 4.1. For calibration purposes, we use the weighted

average of the two unresolved M l y peaks and fit to one (slightly widened) peak at

80.898 keV. Similady, the Ka,- and K,,-sheU X-rays are averaged to 30.851 keV. The

cw decay of 241Am tu 237Np has a strong El branch (E, = 59.5412 keV [54J), providing us with a third calibration point.

The photoelectric effect and Compton scattering are the t m competing processes

for photon interactions over the energy range hv = 30 - 80 keV in silicon. In a

photoelectric process, a K-shell electron bound to the Si atom totaily absorbs the

incident energy; this 'photoelectron' is ejected 6 t h a kinetic energy Te = hv - Be, where Be is the sheli binding energy. As was the case for bariurn, the inner sheli

vacancy is Bled up, but in this case Auger processes are favoured and so the binding

energy is generally recovered. In Compton scatteringt the photon impacts only a part

of its energy to the struck 'Compton electron', the amount of which depends entirely

on the direction of the scattered photon. The result is an energy spectrum that

extends from zero up to a maximum (Te),, < hv corresponding to a backscattered

photon (see Equation (4.12)). For 30 keV X-rays, the photoelectric effect has the

largest cross-section so the DSSSD spectnim contains the large peak at E = hv with

a small low-energy tail arising from Compton coilisions. At 60 keV, these processes

have about q u a i cross sections and by 80 keV the Compton effect is an order of

magnitude larger; since the photoelectron's spectrum is concentrated over a srnall

energy range, the photoelectric peak is still evident in the y sources, although the

Compton tail cornplicates determining the centroid as precisely as with the X-rays.

In addition to those resulting from the photon sources, a large peak refimed to as

the 'pedestal' is evident in the energy spectnim (as in Figure 4.9); this peak occurs when the strip in question did not fire, but another strip triggered the event. For

the charge-integrating hDC1s used, the observed pulse-height of the non-triggered

strip corresponds to the ADC offset and, ideally, would be a 15 function. In ce-

tthis is covered in more detail in 84.3.3 with regard to the on-iine scintillator calibration.

TABLE 4.1: Low-energy photon sources used to provide a . initial calibration of the strip detector.

133Ba

2 4 1 ~ ~

Source

Cs Km, Cs Ka,

r ( W r (Ml)

r (El)

Rel. intensity

0.648 0.351

0.929 0.071

Energy [keVI

30.973 30.625

) 3û.851

80.9971(27) } 80.898 79.6139(6)

59.541

6.0 M) i(KI UO 140 160 Channel number (strip yJ

FIGURE 4.9: Sample fits to the DSSSD energy spectrum of the 7 source 2"h. The data is the coarsely binned histograrn and overiayed is the fit using a function consisting of a Gaussian (photoelectrons) plus a constant low-energy background (Compton electrons). The fitting range is indicated by the Iirics above and below the 59.541 keV pealc.

ality, the pedestai is a Gaussian peak centered at zero energy with a width that

directly reflects the noise in the electronics. The average width For the x-strips is

(O$") = 3.7 k 0.7 keV and that of the y strips (O:=) = 3.9 1 0 . 4 keV. The centroids

of each of the photoelectron peaks as well as the pedestal provide four points which

can be fit to a linear calibration relating the observed pulse height Mth the energy

deposited in the detector.

The Am and Ba sources were placed in front of the DSSSD within a light-tight

and electrically shielded volume: a thin stainless steel cylinder 040 cm x 60 cm (suf-

ficiently large to minimize scattering effects off the walls of the container) with a mount for the B-telescope assembly.

Each peak in the resulting energy spectra of the 48 strips was then individually

fit to a function consisting of a constant background that extends below the mean of

a Gaussian peak (the photopeak) representing the fuli energy reading of the ejected

photoelectron. Fits to the 60 keV peak from 24L,4m in strips xl and y, are given

in Figure 4.9. The pedestal is fit independently by gating on pulser events for the

scintiiiator, in which case ail of the DSSSD strips were read out with zero energy. The

widths, which are calculateci using the ha1 off-iine source calibration, are typical;

the pedestals contribute 3 - 4 keV to the noise while the pulsers are roughly equal

FIGURE 4.10: Energy calibration of the DSSSD strips x2 and y2 using the sources 133Ba and 241~m. The four points used in the fits (given above) consist of the sources listed in Table 4.2 plus the ADC offset. The calibrations have an offset with units of channels and the dope bas units of keV/channel.

$ = (0.890îO.OS)x[cbannal - (55.40î0.23)] \ = (0.741~0.000)x[channel - (97.49tO.E)I

to the photopeak widths of 5 - 6 keV. The fits to the barium peaks were done

in a similar fashion, but in that case a separate overdl constant background was

also required to account for the higher energy photons that Compton scatter in the

detector. The 81 keV photon interacts predominately through Compton scattering, so

the resulting photopeak in the observed spectrum is wveaker compared to that arising

from the Cs Ka-shell photons; these calibration points, therefore, have relatively large

uncertainties in their values.

Using the results of the fits to these spectra, energy calibrations were made using

linear regression on the four points. Figure 4.10 is the calibration for xa and y2

and numerical results of the off-line source calibrations are given in Table 4.2. The

calibration to the strips look reasonable but, as ive will see in the following section,

we can improve the calibrations using the on-line ,f3+ data themselves.

4.2.3 Extended Calibrations

In addition to the inherent resolution, the final energy reading from the strip detector

will dso be affected by systematic deviations in each strip's calibration in many ways.

As we wil l see in $4.2.5, event selection is based upon which and how many strips

pass a cahbrated energy threshold, as well as a m a - u m limit on AE = jE, - E,I,

O 50 XM 130 200 50 100 BO 200 ao Ch~nnd numbar of l k i p x, Channel numbar ot ¶trip y,

F xa/v = 0.81 CL = U J X

/'

4' '

7'. /"

,,.' ;./"

4 y r

t lm+

75 - - 5 f 5 0 - - 3 i 2 s - Y

O -

-25

m.

@ -

- 6 0 - % il

40 - $ g 20-

O

-20 -

xZ/v = 1.04 /' CL = S I X /" Y''

," /'

/' / ,' / ' -.

/ /

./'

. .

x calibration offset slope

(channels) (keV/chan) 58.llf 0.44 0.87kt0.028

55.40f0.23 O.89Of 0,015

43.49f0.27 O.893f 0.018

43.79f 0.18 O.885f 0.012

58.59k0.30 0.848f0.018

62.643~0.30 O.965f 0.023

60.03f0.24 0.982zt0.019

5l.98f 0.40 O.949f 0.030

65.10k0.20 0.816I0.011

65.99f 0.27 0.792f0.014

64.02f0.27 O.837f 0.015

67.49f 0.21 O.786f 0.011

64.04f0.21 O.925f 0.015

6l.74f 0.26 l.OO6f 0.021

6l.O8f 0.25 O.965f 0.019

190.32f0.39 O.685f 0.015

7l.85f 0.25 O.768f 0.012

61.15f0.23 O.8Ogf 0.013

91.98f0.26 O.82Of 0.014

63.54k0.28 0.828f0.016

72.66f0.31 O.8l5f 0.017

63.27f0.35 0.767f0.017

63.57f0.28 0.857&0.017

69.42f0.57 0.736f0.026

y calibration offset slope

(channels) (keV/chan) 77.15k0.24 O.85Of 0.017

97.49f 0.16 0.741zk0.009

75.26î0.12 0.822&0.008

72.62f 0.22 O.805f 0.014

74.98f 0.25 O.768f 0.015

52.98f 0.30 O.854f 0.022

66.82f 0.26 O.8l?f 0.018

75.lif 0.17 O.8l5f 0.011

l23.26f 0.14 O.7OOf 0.007

73.86f 0.28 O.773f 0.017 96.11î0.29 O.792f 0.018

92.87I0.20 O.Xi6f 0.011 42.4110.31 O.807f 0.020

53.46k0.25 O.847I 0.018

86.455t0.20 0.788I0.012

51.93k0.35 O.775f 0.021 72.52f0.28 0.759f0.016

108.56f0.18 O.76lf 0.010

126.26f0.21 O.725f 0.011

55.63k 0.24 O.843f 0.017

59.63f0.28 0.825f0.019

59.94f 0.29 O.8lOf 0.019

111.81f0.21 0.859I0.016

66.13k0.28 0.797k0.018

TABLE 4.2: Fit parameters of the DSSSD strips off-line source calibration. The caiibration is fit to a function of the form EkeV] = slope x (channel- offset).

and so poor energy caiibrations will cut legitimate events. in order to minimize the

differences in each strip's energy reading, we take advantage of the fact that the two

signals in i and $ should be identical, and effectively re-align the strips by forcing

that fact to be true on average. To that end we can use the on-line 38mK data which

is advantageous because they provide a continuous spectrum well beyond the 81 keV

barium peak; the ce-alignment of the calibrations using the data themselves is, by

definition, over the entire energy range of interest. In applying the off-line calibrations to the on-line data, corrections for possible

DC offset aud gain variations in the electronics were made by comparing the peak

positions of the pedestals and pulsers. Throughout the experimental mns, the offsets

of the original calibrations are adjusted by the difference in the pedestal centroids

(over = 5 minute intervals) from the centroids observed when calibrated. Sirnilarly,

the slope of the calibrations was adjusted by the ratio of the pulser centroids. If si, is the pedestal and x",,, the pulser centroid wheu the off-line calibration was done,

then the corrections applied at time t are:

offset'(t) = offset - (xpd(t) - x b ) (4-1)

The calibrations were done only a few days before the April 1999 experiment and

since the DSSSD is an inlierently stable device, these corrections end up being very

small, typically on the order of 0.1%.

After applying these corrections to the 38mK of data, for each x-strip that passed

a low-energy threshold of 40 keV with only one corresponding strip in y, the energies

E, and E, were plotted as in Figure 4.11. Assuming that variations in the y-strips'

calibrations average out, the deviation from (E,) = Ki provides us with a correction

with which to align each of the x-strips to the average of y. In making the fits,

Poissonian statistics needed to be used in order to be able to include the scarce events

at higher energies. Note, however, the extended low-energy tail especially evident in

the edge strip xl (the inner stcips, e.g. x2, are much cleaner indicating edge effects in

the DSSSD). Eue y event in Figure 4.11 is plotted, so this actually only represents

< 10% (' 1%) of the total number of counts in the edge (inner) strips. It is still an N

important concern, however, because this low-energy tail has a stronger weighting in the fits if al1 the data are used, thereby biasing the calibrations to axi < 1 and PXi > 0. In order to minimize this effect, yet still retain the high-energy events, an iterative

method was used: in the first step we assume aXi = 1, ,& = O and fit Equation (4.3) only to events where Ex - 3OkeV 5 Ey _< E, + 3OkeV. Based on the new values of

aXi and a,, we again fit using events where the new [Ep - EkIs 30 keV. This process was repeated until the changes in the parameter values were less than their respective

uncertainties. Table 4.3 lists in detail the corrections to each of the x-strips using this

alignment scheme.

The iterative method used to fit the extended calibrations ends up applying rather

large corrections to the *"'Am and '33Ba calibrations. Generally, the slopes are de-

creased and the offsets increased, but by far more than can be explained by the bias

from the low-energy tail as described above. Most surprishg is the change in the

offset; the pedestal peak is well-defined and if it really does represent zero-energy, one

would expect the ai parameters to be very close to zero. Random changes in the a,,

would be expected (versus a systematic difference) since the larger energy range of

the on-line data is more sensitive to the dope of the caiibrations. The extended calibrations and the calibration of the DSSSD as a whole are therefore not without their

problems, and so the uncertainties quoted by the fit are certainly underestimated.

The extended calibrations are effective in aligning al1 of the x-strips' calibrations

together, which is necessary in order to be able to compare the energies of each equally.

In order to sirnilady place the y-strips on equal footing, we do the same procedure

to re-fit them to the average of the corrected x-strips. The corrections are listed in

Table 4.4 and Figure 4.12 shows the fits to y, and yz. The variance of the points

around the fit is reduced compared to Figure 4.11 because the x-strips have already

been calibrated to a cornmon energy auis. The fit parameters stiU show the same

trends as in the x-strips (& > O and ayi c l), but are not as large or systematic.

The high-energy tails, however, can be seen to still have a bias since they do not

foiiow the fit line to within the quoted uncertainties, again indicating that they are

TABLE 4.3: DSSSD caiibration fits of = (4) = o, x Er, + ai. These fits align the calibrations of the x-strips to the average calibrations of the y-strips. - s trip

- strip -

13

14 15

16

17 18 19 20 2 1

22 23 24 -

F~GURE 4.11: Cornparison of Ex and Er energy readings using the calibrations determineci using off-line sources for strip xi (Mt) and q (right) . The solici iine is the fit Eg = a x Ex + a and the t l i ~ ~ h t ~ l lines contain the fitting region defineci by JEp - E:j_( 30 keV,

underestimated.

As with the x edge strips the y-strips contain a background, but in this case it is

manifest as a high-energy tail. The vast majority of t hese events have too much energy

in jj and correspondingly too little energy in 5. Yorkston, et. al [551 have discussed

such effects in the case where the incident particle was a heavy ion, and they found

that inter-strip events gave cise to pulses of the wrong polarity €rom induced charges.

They performed similar tests wit h 207Bi but did not observe this effect in this case; the

tails seen in our edge strips are not at present understood, but the effect is relatively

small and the events can be excluded in software if desired (see also $4.4.3).

4.2.4 Characterization of the Resolution

The dominant noise apparent in the DSSSD spectra is electrical, but additional com-

ponents mise Erom fluctuations in particle-hole generation and charge collection. As

mentioned eadier, the electrical noise determines the width of the pedestal wbile the

overail inherent tesolution of the detector should be reflected by the width of the

photopeaks. The average widt hs of the 133Ba M 1 -y peaks are 5.6 f 0.5 keV for y and

5.5 f 0.9 keV for x, in agreement with the resolution of these devices as indicated in

the literature [511.

The final resolution of each strip ivas determined by comparing the difference of

the corrected energy reading of a given strip to that of the orthogonal's corrected

energy. This is basically the same procedure as in the extended calibrations, except

this time we just look at the deviations in order to generate an average resolution

hnction. -4s can be seen for x16 in Figure 4.13, the final extended calibration of this

strip versus al1 of those in y still suffers from a slight bias, as is especially evident

from events in the high-energy tail of the peak (above x 400 keV). The dashed lines

above and below EL = Ek are at st24 keV, representing a AE 5 *3gX,, acceptance

for this stcip (see below). The low-energy thresholds are set to 40 keV, well above

the pedestals of the strips. This strip was chosen as the example because it has the

largest offset and smailest energy range as is evident by the saturated ADC readings

at Ex,, x 725 keV. In order to ensure that no biasing of the on-line data occurs due to

such saturated energy readings, a high-energy threshold of at least 725 keV needs to

TABLE 4.4: DSSSD calibration fits of Eii = (Ex) = ayi x hi +hi. These fits align the calibrations of the y-stries to the average calibrations of the (already corrected) x-strips.

strip

1

2 3

4 5 6

7 8 9 10 11 12

strip

13

14 15

16

17 18 19 20 2 1 22 23

24

L

a,, = O.SZ6r0.0006 p,, = 7.0Zt0.11 keV - xZ/v = 0.55 -/

F~CURE 4.12: Cornparison of the energy readings of stries y1 (left) and y2 (right) to that in x. The result of the fit yields EP = ayi EJri +& which aligns each y-strip to the average of the (already corrected) x-stries-

-mo -1 I

O 200 400 600 600 Energy in X, [keV]

FIGURE 4.13: Plot of E:,, vs. ( E i ) - E:,, with the proposed thresholds for the on-line data indicated by the claslieil lines. Strip xi6 has the largest ADC offset and hence smailest energy range; the upper energy threshold needs be placed at 725 keV so as to ensure that no events are off the energy scaie of this the most iimited strip. The solid lines at f 24 keV represent an 2-4 energy agreement condition used to discrimate against noisy events.

be imposed; the threshold may be set lower to value of 400 keV so that the bias from

the irnperfect alignment of the calibrations is contained wvithin the stcips' resolution. The resolution functions defined by:

RZi = (E;, - E;,) and hi = (E;, - EL,)

were generated and a sample of them are depicted in Figure 4.14. The fact that the

Gaussian fits agree reasonably well over the peaks of the distributions, and that they

are nearly centered around zero, is very encouraging. This indicates that the resolution

of the strips is dominatecl by random processes and that the strip calibrations are

consistent. The widths of these Gaussian fits, listed in Table 4.5), average 8.1 keV.

The (relatively) large tails of the edge strips, however, show that they suifer bom

additionai systernatic effects. Since these tails are not a large percentage of the events,

the edge strips can be included in a finai analysis, but one might wish to consider

excluding these events if statistics is not a concern.

atrip: X, 30 mantr: 132579 (795% ot are. total)

L

rnean - 0.OSt0.03 1

mean = Ofllt0.06 - - w- = 8.29a.06

FIGURE 4.14: Overaii resolution Functions for strips xi, xi:! (left), yi and y[* (right). The resolution is calnùated as &, = (EL, - E;,) and Ri, = (Eki - E L ) . The daçhetl Lines are at f 3u of the Gaussian fit (solid Line) , which fit weii over the peak of the distributions; the xi and y1 have especiaiiy large tails arising from edge effects.

- - Strip: Y. Su nanta: (59255 (W.S% of are. total)

r r i

m

na 4

9-- O Ci

M p : K, Su wmts: U22lD (ï9.SX ot ave. totd)

-50 O 50 la -100 -50

Strip: X, rnean - -0.0610.03 JO aiientc US700 0,- = 7.8720.03 (85.8% of are. total)

mean = -0.22*0.06 u , , ~ = 8.5h0.06

O4000- i

U P

I

TABLE 4.5: Final widths of the DSSSD energy readings by comparing x and y energy readings. The average widths are (nJ = 8.07 & 0.18 and (ay) = 8.08 f

- strip -

1

2

3

4

5

6

7

8

9

10

11

12 -

x-st rips

8.29f 0.06

8.14k0.04

8.10f 0.04

8.l4f 0.04

8.Oïf 0.03

8.O4f 0.03

7.96f 0.03

8.OOf 0.03

7.97f 0.03

8.O3f 0.03

7.89f0.03

7.87f0.03

- strip x-strips

7.76f 0.03

7.80f 0.03

7.94f 0.03

8.18f0.03

8.18f 0.03

8.O7f 0.03

8.17f 0.03

8.24f 0.03

8.2lf 0.04

8.35f0.04

8.36i 0.04

8.96f 0.07

Calibrate each strip and impose energy threshold conditions

1 If strips that fired are adjacent, add up their energies to form

1s there only one hit in I "O- a total 'group energy.' Now, and only one hit in .y? is there only one p u p in 5 and

one group in Y?

Veto eveut (miiltiplc Kt)

Accep t evei~t Veto event ( t i t i kriotvri energ)

FIGURE 4.15: Block diagram of the DSSSD analysis scheme. Essentidy, we sirnply require that events in the strip detector are consistent with a single hit, and that the energy deposited in the two sides (2 and y) agree to within the resolution of the strips.

4.2.5 Position Decoding and Analysis Scheme

The analysis scheme developed For the DSSSD relies on two important premises: (i) a

'good' event is one where only one pixel, a single hit in 2i and one in y j , fired and (a) the energy reading in Z is consistent with the energy reading in 6. The first ensures

that one particle went through the detector only once (in particular discriminating

against ps that backscattered out of the scintillator), while the second is a necessary

condition for a final energy reading. A surnmary of this analysis scheme is given in

Figure 4.15.

The fact that the strips are calibrateci allows us to impose energy threshold con-

ditions that applies equally to al1 strips. The first of these conditions is a low-energy

'strip thresholdl that is placed well above the hardware (triggering) thresholds, and

any strip whose energy is greater than this is considered to have fired. Ideally (indeed

most likely), only one strip in 5 and one strip in 9 passes this condition giving us

an event at xp = (i - 12.5) mm, y,, = ( j - 12.5) mm where i, j represent the strip

number of the x- and y-strips that ked. We would like to make this threshold as low

as possible, but we must make sure that it is high enough that we don't have strips

firing due to a random fluctuation above their respective pedestals; if this happens we

wili veto legitimate events as (phantom) multiple hits. With condition (i) satisfied

and the position of the hit knom, we now need to determine the energy the particte

deposited using the two energy readings. As mentioned earlier, the energy in Z should

be the same as $ to within the resalution of the individual strips, so we check to make

sure that they pass an energy agreement condition:

where

and ucUc is an adjustable (user) parameter that determines how tight this energy

agreement must be. The dEIi, dEyi are the la widths of the resolution functions,

as given in Table 4.5. If this condition is tme, then we take the final DSSSD energy

reading to be the average of the two calculated energies weighted by their respective widths:

Events that do not satisfy ( 2 ) are not immediately vetoed because we expect that

,8s will occasionally be scattered into an adjacent strip. For this reason if two strips

fired in, Say x, instead of just one, we check to see if they were xi and xi*,. If so, we

add up the energies deposited in each and weight the position of the hit according to the energy deposited in each, i-e.

and

In this way we define 'group' hits which are treated the same as single strip events:

if there was one group in x as well as one in y, we then check for energy agreement

between the group energy readings and accept the event if it passes.

The most sensitive test of the setting of the strip threshold is again through use

of the on-lie 38mK data themselves; the x- and y-strip positions, combined with

the relative number of single-pixel versus multiple strip events, indicates good noise

discrimination without a loss of good events. Figure 4.16 is a plot of the XDSSSD

position for events in which there was one (group) hit in 5 and a corresponding one in

9 which passed the AEDsssD 5 3uDsssD energy agreement condition. The large peaks of the individual strips (i.e. where no adjacent strip passed the strip threshold) reflect

the consistency of the x- and y-strip calibrations. A poor alignment causes the energy

condition (Equation (4.5)) to veto more events, the number of which would depend

on how rnisaligned a given strip's calibration is compared to the average of the other

side's; this is seen in the position spectrum when the initial off-line calibrations were

used (dashed line, slightly offset for clarity). The extended calibrations can be seen

to remedy this situation by making these peaks much more homogeneous. Almost 7% of the events that would otherwise be vetoed are retrieved once the strip calibrations

are ptoperly aligued and, more importantly, the efficiency of the DSSSD is rnuch more uniform across the strips.

The distribution of the inter-strip events is less sensitive to the relative consistency

of the calibrations; the shape of the distributions for the off-line and extended cali-

brations is very similar as seen in Figure 4.16. These events are, however, sensitive to

the applied strip threshold; if set too low, a strip adjacent to where the P left (au of its) charge is more Iikely to fire from random fluctuations above threshold. This will bias the shape of the inter-strip events towards having too many events just below

the main single-stcip peak (there is not a corresponding bias just above because of

the choice of binning in this figure accentuates the very low Ei-l, while the corre-

sponding Ei+l is absorbed in the main peak). Alternatively, if the threshold is too

high, we would also see an overali l o s of events because the cases where only a small fraction of the charge went into the adjacent strip would be less likely to p a s . For

example, if 100 keV is deposited in xi and 40 keV in ~ + l (with the fuil 140 keV in

y j ) , a threshold of > 40 keV would not add back the ~ + l energy back and may veto

extended - - - OU-iine 1

- 10 -5 O 5 10 Position in x [mm]

FIGURE 4.16: Position of DSSSD P hits in 5 fiom the on-line 38mK data. The claslied line corresponds to the initiai photon calibration while the solid uses the extended caiibration. Note the improved hornogeneity in the nurnber of counts of the individual strips (linear scale, above) as well as the symmetry of the inter- strip hits (logarithmic scale, below). The corresponding spectra for ?j shows sirnilar characteristics.

the event since Ex, # E,,.. Thus, too high a threshold suppresses events near (i f 6) where b c 0.5, but wvill not seriously affect events near the midpoint since these leave

nearly equal amounts in each. Tbe shape of the inter-strip events (averaged over al1

x-strips) are plotted in Figure 4.17 and shows how the data are affected by the value

of the low-energy strip threshold. The lits, which are to a quadratic function, are

aU in agreement with the data eircept for the hst point; the 20 keV threshold is too

low because it allows too many events here while the 65 keV one is clearly too high.

Between these two thresholds, the shape and even the overall number of counts is seen

to be relatively insensitive to the value used. The large 65 keV threshold is clearly ex-

cluding events where a small (but real) amount of charge was deposited in an adjacent

strip. By looking at plots similar to Figure 4.16, but with h e r steps in the low-energy

threshold, it was found that the inter-strip distributions were constant over the range

35 - 55 keV. The results containecl nrithin this thesis ail use a low-energy threshold

of 40 keV.

20 keV threshold 35 keV threshold

a Li

A 50 keV threshold O 65 keV threshold

i 1 I I I

0.0 0.2 0.4 0.6 0.8 1.0 Inter-strip position [mm]

FIGURE 4.17: .Average position of inter-strip DSSSD events using different low- energy thresholds. When the threshold is too low (20 keV) , we see too many events below the single-strip peak and if set too high (65 keV), events to either side of the main peaks are reduced. The lines are quadratic fits to al1 but the lut point.

As mentioned in $4.2.1, a charged particle such as a relativistic positron loses energy

through multiple Coulomb scattering, which is an inherently random process. The

energy deposited by the positron will depend on the angle(s) it is scattered into and

how long the random walk through the detector is; the energy density distribution

follows a Vavilov distribution 1561 which contains a large peak corresponding to parti-

cles which suffer only small angle scattering, as well as a high-energy tail for the ones whose random waik through the detector is relatively large.

The on-line 38mK data in Figure 4.18 show the final DSSSD energy reading as

analyzed according to the scheme outlined in 84.2.5, and are compared to a GEXNT \

simulation. The Monte Car10 has been renormalized so that the peaks of the two

spectra are equal. Both the simulation and the data have the following conditions

imposed:

a 40 keV low-energy DSSSD threshold (from the previous section).

- MmK data

GEANT MC

moment 1 data MC

mean 175.2 164.9 st. dev 53.2 48.5

skewness 2.02 2.35

FIGURE 4.18: DSSSD energy spectrum of the on-line 38mK (solid Line, al1 stries) and the comparison to GEANT simulations (llii~ti('tL). The first three moments of both distributions are given to characterize the ciifferences.

a 500 keV high-energy DSSSD cutoff (to reduce b i s as noted for Figure 4.13).

an Ex, - Eyj energy agreement condition using rCut = 3.

a 2500 keV low-energy scintillator thresholdt

There is a clear discrepancy between the experimental data and GEANT with a

> 10 keV difference in their average energy losses; the table in the figure lists the first,

second and third moments of the two distributions. The sharp rise on the low-energy

side of the peaks agrees (up to a constant shift) and this shows that the simulated

data have had the detector resolution properly incorporated. The high energy side of

the peak is clearly sharper in GEANT, and this may be indicative of an underestimate

in the nurnber (or angle) of scatten within the DSSSD. Part of the problem rnay arise fiom the extended cdibration corrections (of §4.2.3), and simply be a probiem with

tthis condition on the E detector's energy reading eluninates the 38K ground state 7 contamination, which is not indudeci at this stage of the analysis (see 84.3.5 and beyond).

the overall calibration. Spectra of the individual strips are al1 aligned by virtue of

the resolution functions being centered about zero, and therefore the data are not

wider due to strip calibration variations. If the difference were solely due to the

overall calibration, then it could be corrected by fitting the data to the MC, with the

energy scale free to vary. Attempts to do this did not fully correct the situation as

the high-energy side of the peak remained underestirnateci, so it is more than just the

calibrations.

At this time, we do not fully understand this difference, but we do know that

in relation to the telescope's total E i- A E energy reading, this discrepancy is very small: at 1 MeV, the average difference is only 1% of the total and it is only 0.2% at

5 MeV. The impact on simulations of the scintillator's spectrum, which must include

the energy lost in DSSSD, is discussed in 54.4.1, and 84.3.5 shows that the total energy

spectrum is well reproduced if the average difference is considered. It is therefore not

crucial that we resolve the discrepancies found within this section, but improvernents

can be made in the understanding of this device if more careful calibrations are made.

The full energy peak of a conversion electron source, such as 207Bi, would help to provide a cleaner initial calibration which would make the extended calibration easier

and presurnably involve smaller corrections. The source must, howvever, be open

(unlike the one used throughout this thesis) so that the electrons do not suffer (much) energy straggling before entering the DSSSD.

4.3 The Plastic Scintillator

This part of the p-telescope is important to TRINAT'S B decay experiments because

it provides the (rnajority of the) energy measurement of the emitted positron and the

time of the event relative to the recoil detector. It has been my hope from the start

of my studies to design and optimize the scintillator weil enough that the energy and

timing resolutions do not limit our measurement of the correlation parameter. The

timing of the scintillator wiii be shown to be good enough that our recoil time-of-

mght measurement is b i t e d by the trap size. Preliminary tests [5fl of our sensitivity

to uncertainties in the calibration of the gain indicate that Au, = 0.1% for a 0.1%

change in the slope of the gain. As anyone who has worked with ,Bs wiil appreciate,

this represented a formidable task.

4.3.1 Optimization

The block diagram of Figure C.l in Appendix C (page 123) outlines the scintillator's

electronics. The energy signal is taken from the dynode output of the PMT and

inverted through a LeCroy 428F linear fan in/out. The anode provides the timing signal to the Tennelec 455 constant fraction discrirninator which is used to set the

scintillator's hardware threshold to approximately 300 keV. The stabilization unit,

discussed in greater detail later (see §4.3.4), minimizes gain variations by monitoring

a LED's pulse-height in the PMT. Once the scintillator and its electronics were assembled, tests were performed to

determine the wrapping that would best collect light in our geometry. The wcapping

of the scintillator can be broken up into two areas: the front face of the plastic,

and the wrapping around the side of the scintillator and light guide. For the front face, extra care was taken to minimize the energy straggling of positrons as they

enter the scintillator. To that end, 207Bi spectra obtained using a Si detector were

compared when sheets of different wrappings were placed in front it. 207Bi decays via orbital electron capture [581 giving two mono-energetic internal conversion electrons

at 975.6 and 1048.1 keV, which are resolvable with the Si detector. Comparison of the

energy loss effects of different wrappings and thicknesses could then be made using the

peak-to-valley ratio of these two peaks. This was done for aluminized mylar (Al on

C5H4O2), Teflon (CF2=CF2), white paper and Tetlart, the results of which indicated

that Teflon [59j caused the least amount of energy loss and straggling.

Figure 4.19 shows the spectra of a 207Bi source using a few of the wrapping schemes

considered. Once again, the diffuse reflector Teflon was found to be best suited for

our geometry because it was with this wrapping that we observed the lacgest signals.

One can see that Teflon around the sides clearly yields better overall light collection

compared to Ai mylar. With Al mylar only on the fiont face, the same overall gain

is observed as the Teflon (once enough layers was applied), but one can also see the

+This is nomally used to keep scintillators light-tight, but these tests indicated that it adds to the energy straggling of the incident particle and so was not used,

- A l mylar Al mylar % .

- 1' ! - - - - Teflon (xl) Tellon l Al mylar Tellon l .!, I La .: 1 . . . . - . . - Teflon (x4) Tel lon m .

! . , .: d 10' : f

T 1

200 400 600 800 1000 Channel number

F m RE 4.19: 207Bi spectra using different scintillator wrapping schemes. The Teflon wrapping around the sides of the scintillator and Iight guide c m be seen to provide the greatest light collection; aluminized mylar on the front face yields the same light collection efficiency, but Tefion minimizes the energy straggling of the electrons as they enter the scintiiiator.

energy straggling effects in the electron conversion peak. For this reason, the final

wrapping of the plastic and light guide wvas done entirely with Teflon (as specified in

GEANT'S geometry on page 40).

4.3.2 Timing

Good timing resolution between the recoil and P detectors is essential for accurately

determining the recoil momentum from its time-of-flight. To understand the tim-

ing characteristics of the scintillator, tests were perforrned !vit h anot her scintillator

(04 cm x 4 cm) using a 22Na source. When placed between the two scintillators,

the back-to-back annihilation radiation from the P+ decay of this source allows a

measure of the relative timing between the two detectors. The resulting timing peak

had a FVmI = 0.9 ns which, assuming both scintillators have equal timing, gives a

a,, x 0.4 ns.

It is the relative timing of the scintiiiator with that of the recoil detector that

is relevant to the experiment and, since the MCP does have a small efficiency for

4 I I

a,, = 1.00*0.09 ns

FIGURE 4.20: Relative timing between the P-telescope and the recoil detector using an source (left) and the on-line data (right). Both fits yield a scintillator-MCP timing resolution of ust 1 ns.

detecting ys, tests using a source were made using the essentially coincident

emission of the 898 and 1836 keV lines. An 8 ns delay cable was added to the

scintillator's timing half-way through the test in order to allow an easy channel-to-

time calibration. The results of a double-Gaussian fit to the two peaks are depicted

in Figure 4.20 (left) and give a relative scintillator-MCP timing, a&, of about 1 ns.

The timing from scintillator-MCP coincidences in the on-line data contains, in

addition to the Ar recoils, a peak at zero TOF. This 'prompt peak' (right of Fig-

ure 4.20) is thought to arise €rom events where one of the annihilation ys hits the

recoil detector; if an electron is ejected in one of the channels, the MCP will register

it as a hit. The prompt peak's energy spectnim in the scintillator is badly distorted towards lower energy, indicating that the other annihilation quantum is what pre-

dominantly fired the 0-telescopet. The events above 511 keV probably correspond to

the positron backscattering off the MCP and then into the telescope (the transit time for a relativistic B is 0.35 ns).

The tail at longer TOF (103410 ns) may corne Çom events where the positron

+A DSSSD coincidence is required in thh timing spectnun.

fires the P-telescope and this tirne a low-energy photon produced by the decay fires

the MCP. The daughter Aro atom has a good probability of being left in an excited

state (11 eV) after the 0 decay; these excited states decay to the ground state by the

emission of a W photon.

The fit to the prompt peak is a Gaussian plus two exponentid tails with decay

times of 2 and 8 ns (for the atomic excited states), d l with free normalizations. This

fit agrees with the '*Y measurement and so we take our detector TOF resolution to be O T ~ F = 1 as.

In the @ - v experiment, the resolution of the deduced energy of the recoil is

dependent not only on the relative timing of the detectors, but also on where the

decay occurred. The size of the trap affects the uncertainty in the position of the

decay (which is assumed to be the trap center) and hence the distance the recoiling

atom transverses before firing the MCP. With the typical trap dimension of 0.5 mm along the detector auis and considering the fastest recoils (Ar+4*+5~--.), this efTect adds

a f 4 ns 'time jitter' which is greater than the detectors' relative timing resolution.

The timing characteristics of the P-telescope are therefore adequate for the energy measurement of the recoil by TOF. If the trap size can be reàuced by a factor of four,

however, the uncertainty in the scintillator's timing will become significant. -4nother

reason for trying to improve the timing resolution is to use the 38mK measurement

to deduce the trap size; this could then be compared to that obtained using a CCD camera, which is not without its own systematic errors.

4.3.3 Energy Calibrat ion and Resolut ion

The largest systematic uncertainty in the @ - u experiment introduced by the B- telescope is the energy calibration of the plastic scintillator, and therefore considerable

effort was directed toward understanding it as completely as possible. Unfortunately,

a well-characterized source of mono-energetic positrons between 1 and 5 MeV is not

readily available at TRIUMF, so the calibration tvas done by fitting the Compton

edges of various y sources.

The analysis of the Compton spectra was performed using two schemes: fitting

the data analyticdly to the Klein-Nishina formula, as well as fitting to a Monte

0 .O O .S 1 .O 1.5 2.0 Compton electron energy [MeV]

FIGURE 4.21: Kinematics of the Compton effect aad the energy spectrum of the Compton scattered electron for an source (ET = 0,898 and 1.836 MeV) and a an annihilation quanta (ET = 511 MeV). The solicl line is the Klein-Sishina calculation and the dashed lines represent GEANT simulations.

Car10 simulation. Agreement between the tnr, methods served as a consistency check,

but the detailed analysis was limited to the Monte Carlo fit sirice the analytical formula does not indude multiple scattering, surface effects, 6 rays, and otber effects

contributing to the low-energy tail below the Compton edge.

The energy calibration is assumed to be linear (see 8.4.1) so that the observeci

pulse height, X ~ C , c m be caiibrated using:

Here xo is the ADC offset and X has units O€ channels/keV.

The dominant component to the spectrum of 7's in plastic is the Compton effect

( c . photoabsorption in a Ge(Li) or Nd scintillator) which is the inelastic scattering

off an atornic electron that is assumed to be free, as depicteci in Figure 4.21, The

energy of the Compton electron foLlows from energy-momentum conservation and

depends only on the direction of the scattered photon:

7i-aey2(l - COS 0) = l + ? ( l -ms0)

with y = E,/m,. The photon w i l transfer the greatest energy when it backscatters

(cos0 = -1) so that the maximum energy in the Compton spectrum occurs at the

so-called 'Compton edge': -

To calculate the differential energy spectrum of the Compton electrons, we turn

to the quantum mechanical calculation of Klein and Nishina [601. Letting s = T,/E,, the result is:

where r, = e2/4neome = 2.818 fm is the classical electron radius. GEXNT uses

Equation (4.13) to simulate Compton scattering, and one can see the comparison

of the Klein-Nishina formula with simulations in Figure 4.21. The extra bump at

energies above the Compton edge anse from events where the y bas scattered more

than once within the scintillator. A larger low energy tail is evident due to particles

escaping before depositing their full energy as well as from electrons that Compton

scattered from various neighboring volumes before entering the scintillator. The effects

of bremsstrahlung in the low Z scintillator at these energies is small (see Figure A3),

but is calculated in the Monte Carlo.

The final fitting function for the y calibrations needs to account for the resolution

of the scintillator whidi depends on the number of generated scintillation photons,

the number of these collected on the photocathode, noise in the electronics and in-

homogeneities in the plastic. If we assume that the width is dominated by photon

statistics and is therefore Gaussian, we use a function of the forrn [611:

where p and uo have units of keV. The noise introduced by the electronics, no, is

reflected in the peak observed when the scintillator does not fire (the pedestal).

The distribution used to fit the 7 calibrations is the convolution of the Monte

Car10 simulation with the resolution, Equation (4.14), Le.:

The parameters free to Vary in the fit to data are the energy calibration (x,, A) and

the width of the resolution (a,, p ) , The overall normalization is h e d such that the

data and simulation have an equal number of counts over the fitting range. Fits to

88Y are given in Figure 4.22 and are seen to agree well when the fitting range is

limited to just the Compton edge itself (top and middle; the arrows denote the low-

and high-energy Iimits of the fitting range). The events above the Compton edge

arise from cases where the 7 Compton scattered more than once in the plastic, and

this effect is generally reproduced in the MC; for the low-energy 7s (511 of 22Na and

137Cs), the MC does not do as good a job. The fit to the whole spectrum (bottom)

is not reproduced as well, and the resolution is forced to increase to help compensate

for this fact. Note, however, that when both edges are included, the offset and slope

can be simultaneously fit and that the fit values for the calibration do not change

much. The correlations between these parameters (as well as a, and p) , however, are

as large as 90%; the results can depend strongly on the initial guesses for their values

and so the results are not reliable. We must therefore fk the offsets xo and o, when

fitting the spectra and should only fit over the Compton edge itself where the MC reproduces the data well. As an initiai guide, the parameters xo and a, are taken to

be the centroid and width of the pedestal.

The channel nurnber, xmc, and width, asin, at each (Te),, are calculated using

the fits to X and p from the y sources: 22Na, 88Y and I3'ICs. These six points+

are then used to fit Equations (4.10) and (4.14) which then give the first iteration of

the calibrations: dl A', d, and p'. In this case, the offsets, xQ and a,, are free to vary and so are fit, even though in fitting the actuai y spectrum they are always fùred.

The y spectra are then re-fit with these new values of the offsets fixed, and the whole

calibration process is repeated. This iterative method is continued until changes in

the fit values become negligible.

tThe two lines in '%O are not resoIved by the scintillator and so only constitute one fitting point.

1400 1 L

x, - 43s channels

1200- A = 294.23IO.41 ch/MeV 3 E p = l.69IO.W keV 0 1000' x'/v = 1.1a3 CL. = 20% O ~i 800 - O

600 - al O E 400 - 1 2 200 - I b

L

x, r 43.50 channels

m 1200 A - 295.8310.32 &/MeV 4

p = 2.0210.14 kaV 2 1000 - l -- x2/v = 1.1002 C L . = 21%

O c 800 O I 115LI keV cl 600 - ' 400 Ei I 1 2 200 - I

1

O -* )r

FIGURE 4.22: Fits of a 88Y Compton spectnun to a GEANT simulation. The fits are to the 898 keV 7 (top), the 1836 keV 7 (middle) and the whole spectrum (bottom). The solid line is the MC over the fitting range (indicated by the arrows) and the dashed shows the rest of the hilC spectrum.

O Q I O min rn 22 2 23 2 V O in rD 9k 9 k * F 3'pc c3 m o * 010 in * C i 1 a) -im m m i n ri

n m O O* MS eu I.@? 0 @!O 4 Nrc eu 4 4

Nin rn ma) rc ?* e? @?Y m 3 0 O O 0 O

N O e3 u 3 Q ' i n q'? -! k'3. F9 nt- ri m o * z g m 3% 2

Table 4.6 lists the results of such fits for two iterations of a calibration for the

Aprill999 experimental runt The fit to the calculated X A D ~ of the 2" iteration and

the residual plot are given Figure 4.23. If we are interested in calculating the energy

for a given channel number, the calibration in the figure is expressed as:

The solid lines in the residual plat are the uncertainties in the calibration as given by

the above expression. The discrepant point at (Te),, = 1.94 MeV is from the Comp

ton edge of the 38K 2.2 MeV y. This Compton edge could not be fit well because of the

large 38mK 'background' which needed to be included in the fit; as will be mentioned

later, there appears to be a 2% discrepancy in the scintillator response between ys and

/3s and so simultaneously fitting the B spectnun will necessarily bias the Compton

edge fit. This point was therefore not included in the fit to the calibration.

Over the limited range that the y sources cover, and neglecting the poor 38K result,

the scintillator is found to be linear and calibrated to within f4 keV. Indeed, since

the experimental region of interest extends out to 5 MeV, ive still must be concerned

about the linearity at higher energies. G 24L.4m/Be source is normally used for the

neutrons it produces via the gBe(a, n)I2C reaction, but attempts were made to use

it as a 4.44 MeV y source from when carbon atoms left in the excitecl state decay

back to the ground state. The neutron background, much like with the 38K, made the

fit to the Compton edge unreliable. Still, to give some understanding as to possible

non-linearities in the scintillator gain, Figure 4.24 is a plot of a fit to the Compton

edges of the lower-energy ys as weli as this 241,b/Be source. The solid line represents

a linear fit through ail the points while the dashed line is a fit with the non-linear

calibration given in the figure. The diierence between the two types of calibration is

seen to be less than f 25 keV which should be a conservative upper limit considering

the poor fit to the 241,4m/Be source. Clearly, it would be desirable to add points

between the 88Y (1.9 MeV) and 24LAm/Be Compton edges to better determine the

linearity between 2-4 MeV.

Returning now to the results of Table 4.6, the resolution was fit to the Uxin of

the 2nd iteration with the results given in Figure 4.25(a). The 38K and 241Am/Be Compton edges are plotted, but not included in the fit (the 241,4m/Be was taken from

x,, = (43.010.3 ahan) + (296.210.4 ch/MeV) x T,

O 200 400 600 8ûû 0.0 0.5 1.0 1.5 2.0 2.5 Channal number (TJ,, [MeVI

FIGURE 4.23: Calibration of May 2nd, 1999 using the Compton edges of the sources listed in Table 4.6 (left) and the residuals of the fit (right). The additional point at 1.94 MeV is the 3BK ground state, but this was fit with a large 38mK ,û 'background' and subject to systematic errors; this point was therefore not included in the fit. The stdi$l lines in the residuai piot represent the uncertainty in the calibration.

(243.2k0.9 &/MeV) x T, Channel = (38.8*0.6 chan) +

1 + T-df(2.50~0.55)xl~2 MeV]

FIGURE 4.24: Non-linear fit to the scintiilator's calibration using the Compton edges of 7 sources. These calibration points and those of Figure 4.23 were taken at mirent t h .

Figure 4.25(b); see below). Additionally, the result quoted by Cliflord, et. al 1431 is

included for cornparison; as indicated by the design simulations, it was hoped that

TWNAT'S scintillator would have a resolution comparable to Clifford's, and it c m be seen that this has been accomplished. At least over the range of the 7 sources, the

resolution follows the square-root law expected if photon statistics dominate uncer-

tainties in the scintillator's energy measurement. The fits actuaily tended towards a

negative offset, i.e. usin - d x - O,; as this is unphysical, the fit was forced

to og = O if it converged to negative values. The width of the Compton edge at

lower energies is more dependent on multiple scattering effects as the y cross section

is increasing; this complicates deriving the resolution for 13?Cs and the annihilation

radiation from 22Na, and tends to overestimate the ad, of these pointa When u, = 0,

the fit value of p will increase in compensation, so that the resolution given in the

figure is not underestimated, though it may in fact be ouerestimated,

Figure 4.25(b) is a fit to the same 7 sources (except 13'Cs \vas not included) when

the spectra were taken off-line in an environment where scattering off nearby volumes

was minimized. The fits to these spectra provided cleaner spectra that could be fit

further below the Compton edge than those taken when the scintillator was mounted

in the detection chamber. The dashed line of this figure represents the fit if the

*'"Arn/Be edge was not included; the solid one, whose results are the ones quoted, is

if this higher energy point is included. The result, which is in agreement with that of

the April 1999 fit, is only slightly affected by the 241Am/Be point due to the relatively

large uncertainty in its value. The resolution of the scintillator is therefore taken to be

Gin = d(1.80 keV) x Tsin- It is this resolution function that is used in subsequent

MC simulations.

4.3.4 Stabilization

As mentioned earlier, the gain of the PMT is stabilized to correct for long-term drifts,

changes in count rates, and temperature variations. The system is schematically

depicted in the lower left part of the electronics diagram (page 123), and further

details about the 'stabilization unit' can be found in reference [621.

-4 blue LED is rigidly coupled to the light guide of the scintillator just outside the

(a) April 1999 (b) November 1998

FIGURE 4.25: Resolution of the scintilator as determinecl by fits to Compton edges. The 38K and 2 " . h / ~ e points are not included in (a) because their Compton edges are on top of a large background (ps and neutrons respectively) . The result quoted in (b) includes the 2 4 1 h / 8 e point (solid line) and does aot change the result much from just using the lower-energy ys (dashed line in (b) and result given in (a)).

vacuum system as well as to a photodiode (PD) via a fibre-optic cable. The intensity

of the LED is locked by the stabilization unit which adjusts the power driving the LED

such that the signal in the PD is maintained constant. The temperature dependence

of the PD'S gain was measured to be -O.l%/"C, so large temperature changes would

not be properly corrected for. Although TRINAT uses a temperature stabilized clean

room (f0.5"C to help keep temperature drifts in the Ti:sapphire laser intensity from

extending beyond the feedback loop's range), we decided to house the PD in a casing

stabilized with Peltier coolers to f 50 mK. Thus the LED light output is constant at

the 1 x l ~ - ~ level.

The gain of the scintillator is monitored by the unit and stabilized by locking the

LED pulse height in the PM% this is done by adjusting the (nominally -1850 V) high

voltage applied to it. The 450 nm wavelength LED was specially chosen (versus more

FIGURE 4.26: Stabilization test of the scintillator's gain. Plotted I the peak position of a * 0 7 ~ i source in the scintillator over the course of hours. The system can be seen to keep the gain of the PMT constant even when subject to large count rate changes and temperature variations.

0.950 -;

readily available green LEDs) to closely match the spectrurn of the BC408 scintillation

light as well as to overlap the peak of the photocathode response (both 425 nm). This

is important to ensure that the spectral sensitivity of the photocathode to the LED and scintillation light be as closely matched as possible. Also, since the temperature

dependence of the photocathode's quantum efficiency is a function of the incident

photon's frequency, good overlap ensures that temperature variations are properly

corrected.

Tests of the stability were made using the electron conversion peak in 207Bi. The

scintillator, unlike the silicon detector used to test for energy straggling, does not

resolve the two iines; the spectrum has just one peak at roughly 1 MeV. The 207Bi

decay also has a few y lines, but a coincidence condition with the DSSSD removes

this background; the fuil absorption peak of the mono-energetic positrons is a nearly

Gaussian distribution, which is a good monitor of the PMT gain. The results of one

of the stabilization tests, when the detector was subjected to large changes in the

count rate as well as the ambient temperature, is given in Figure 4.26. The rates were

rtandard deviation of points = 0.40%

1 5 r

O 1 2 3 4 5 Time [hrs]

O 1 2 3 4 5 Time [days]

FIGURE 4.27: Long term test of the scintiilator stabilization system. The count rate was a constant 750 Hz and temperature variations are las t h a . 0.5'.

changed by introducing y sources ('37Cs and aCo) which do not contaminate the

electron conversion peak again because of the DSSSD coincidence. In the experiment

the count rates only Vary from 100 - 500 Hz, predominantly due to changes in the

amount of 38K background. The test dernonstrates that, after an initial jump, the

stabilization system adequately corrects the PMT's gain when subject to count rate

changes 5x larger than we see in the experiment.

The temperature dependence of the system was investigated by adjusting the

ambient temperature of the TRINAT laboratory by 3"' which again is much larger

than experienced during the correlation experiment. As it did when the count rate

was tested, the stabiization system recovers shortly after an initial jump, and correctly

locks the gain.

The overaii stability of the gain including large count rate and temperature changes

is 0.4%. With only small, long-term drifts in the temperature and a constant count

rate of 700 Hz, the long term stability was tested over a period of four days Mth the

results given in Figure 4.27. Though the gain shows a dehi te drift of approximately

-O.4%, the short term variations in this case are seen to be as low as 0.05%. The

Compton calibration has an uncertainty of 0.14% (extrapolated to 5 MeV) so the

stabilization unit corrects the gain well enough considering how weii we can measure

the energy.

Approximately every three days during the April/May 1999 nui, calibrations using

nNa and 60Co were made so as to monitor the long term drift of the scintillator

gain. The differences in these calibrations are only about as large as the uncertainties

in the fits themselves, and so the system is stable to within our ability to measure it

this way. Increased sensitivity to long-term drifts rnight be obtained by comparing

the scintillator's on-line ,û spectrum as a function of time. Indeed, as we will see

in the next section, the final calibration of the scintillator is taken from fitting the

/3 spectrum of the entire data set. By doing this, we become less sensitive to the

long-term drifts because in this case, the calibration is fit to the gain averaged over

the entire running period.

4.3.5 38mK Results and an Extended Calibration

The on-line spectrum of the scintillator on its own, despite the 75 cm collection-

detection trap separation and the lead shielding (both of which help greatly), is still

dominated by the 38K background. The y-@ ratio in the pre-scaled scintillator spectrum was measured to be 45:l by simultaneously fitting the Compton edge of the

2.2 MeV 7 and the 38mK /3 spectrum to GEANT simulations of the two. The hard-

ware DSSSD coincidence greatly reduces the ground state background by a factor

of 35, but the y events cannot be totally removed this way because t hey do in fact

have a non-negligible probability of firing both detectors in the telescope, The most

likely mechanism for these -y coincidences is when the photon Compton scat ters in the

DSSSD and the collisional partner, the electron, is cletected in the nearby scintillator;

both detectors in this case register an event which is thus inàiscernible from a (good)

B event.

Here and throughout the rest of this section, the scintillator spectra presented

require a coincident DSSSD event that passed the analysis scheme outlinecl in i4.2.5. This condition, which can also be imposed in simulations, is used because it provides a

cleaner ,û spectrum by reducing the 38K background; however, the 2.2 MeV ys do fire

both detectors and so will d l need to be included in the analysis as a background.

The shape of the on-line /3 spectnun, particularly the iow-energy part of it, was

founci to have a strong dependence on the conditions imposed by the DSSSD anal-

ysis scheme. In order to get 95% of the events in the resolution functions of the

strips, a a,,, = 3 energy acceptance should be chosen (see Equation 4.5 on page 57).

By definition, the variation of the energy reading in the A E increases with the

AEMssD 5 SaDsssD acceptance, and the suppression of background events will be less efficient; note also, however, that it tends to accept more higher-energy DSSSD

events (2 500 keV) since these events are the ones which suffer most from inconsis-

tencies between the strip calibrations (see for exarnple Figure 4.13). More precisely,

a tight cut of ~ u D ~ ~ ~ ~ will aclude (goodt) higher-energy DSSSD events whereas the

larger acceptance retaàns them. The plots in the top of Figure 4.28 show the Kurie

plots$ for the different DSSSD energy agreement conditions of luosssD, 2oDsssD and

30DsssD. The tightest condition, AEDsssD 5 la^^^^^, ~ C C O U ~ ~ S for 68% of the 3aDsss~

overali acceptance; the (1 - 2)UDsssD and (2 - 3)uDsssD events contain the additional

26% and 6% respectively. In order to compare the spectrum shapes (bottom of the

figure), the spectra have been renormalized so t hat they al1 have the same totd num-

ber of counts and then the difference from the average was taken. The spectrum

shape of the 2~~~~~~ events is not dramatically different From the tight ~ u D ~ ~ ~ D cut,

but does have slightly more events at lower 0 energy. The 3sDsssD events have a

very different shape which is e-upected, whether the loi-energy events correspond to

hi&-energy DSSSD events or to a background; 84.4.1 discusses the total (E + 4E) energy reading which discriminates between these two cases. -4s statistics is not a

concern in the P spectra from the April/May 1999 nin, a DSSSD energy agreement

condition of lapsssD is used throughout this thesis unless otherwise noted.

GEANT simulations of the 38mK decay were programmed [63j to generate the initial

positrons (as well as the recoils) from the trap* according to the decay rate, Equa-

tion (2.24); the Standard Mode1 values of the Cs = Cb = O and CV = C l = 1 are

(always) assumed. The ps are emitted isotropically into 47~ and tracked until they

either annihilate or exit the detection chamber. h y generated secondaries are also

Eully tracked to ensure the simulation properly accounts for coincidences where the

+'Goodt in that it was an e* which fird the DSSSD; it will be 'baà' in that we wiU have a large uncertainty in the overaii energy,

*The response function is not accounteà for in Figure 4.28 so as to show its dects. 'The finite size of the trap, as measured by CCD cameras, is incorporated in [631.

FIGURE 4.28: Scintiilator Kurie plots for different DSSSD x- and y-strip energy agreement conditions. The Kurie plot with AEDsssD 5 3Cq)sss~ follows a straight line above the 2.2 MeV 7 background; the events above the end point (nominaily 4.75 MeV, which is below the Q-value because of the energy lost in the Be foil, DSSSD and Teflon) are from Compton sumrning of the annihilation radiation. A DSSSD energy agreement condition set between (2 - 3)cQsssD does not contribute many events compared to the rest (top), but have a much larger low-energy tail (bottom; renorm&zed).

scintillator and/or DSSSD only fires as a result of the annihilation radiation or a 6 ray

that goes kom one into the other. The scintillator and DSSSD singles spectra are in-

cremented by the total energy deposited in t hem by eit her the primary pwit ron or any

generated secondary. If the simulated energies deposited in the detectors both pass

their respective t hresholds, as defined by t hose used in the experimentd data analysis,

t hen the telescope's singles (i.e. the Tp = Tsin + EDsssD coincidence) spectrum is also incremented.

Simulations of the 38K decay were made in an attempt to generate the shape of the

y background. The MC generates the 2.2 MeV photons at the collection trap since

this is where most of the ground state's activity is concentrateci. In order to speed

up the simulations, the 7s are not emitted isotropically, but are initially directed

towards the 0-telescope in a cone that covers the area exposed by the 15.24 cm

diameter detection chamber. The Monte Carlo does not contain any volumes outside

the detection chamber, but it is important to start the .ys from the first trap because

they can (predominantly forward) scatter in the chamber wall and this probability

will depend on the initial direction of the y. The lead shielding is not included because

the CPU requirements would be exorbitant; this will certainly affect the simulated

38K spectrum shape because the ys that (fonvard) Compton scatter in the lead (and

then detected in the telescope) wvill appear as a source of ys that are distributed with

energies less than the original 2.2 MeV. The Kurie plots of the scintillator's on-line @ spectrum in Figure 4.28 c m be seen

to be linear above about 2.2 MeV. The deviations are ptedominantly due to the 38K background, but effects from the response function of the scintillator must also be

included. The response function effects are most clearly visible as the high energy

tail near and above the end point, and by the large number of events just above

threshold; the former is from Compton summing of the annihilation radiation while

the latter arises from events where the positron was stopped in the DSSSD and one

of the annihilation quanta Compton scattered in the plastic. Bath of these effects are reproduced in GEANT as can be seen in Figure 4-29; this is a fit of the data to MC simulations of the 38mK spectrum and the ground state's (coincident) 7 background.

The Compton edge at 340 keV corresponds to the 511 keV annihilation quanta and

has in fact allowed us to keep the offset and the slope of the energy calibration

A = 289.5910.0 &/MeV x2/v = 1.tû64 CL. = O

FIGURE 4.29: Fit of the amK spectrum to a Monte Car10 simulation that includes the 2.2 MeV background. This spectnun represents the energy deposited in the scintiiiator (only) detected in coincidence with an event in the DSSSD. The clasiictl line represents a simulation of the /3 spectrum and the 6iied curve is the 38K gound state background. The sdid line is the sum of these two simulations over the fitting range (304 - 5204 keV, over the entire spectrum).

both free to vary in the fit because we bave two distinct points in the data: this

Compton edge and the known Q-value of 5.022 MeV. Note that the /? spectrum only

appears to extend al1 the way out to the Q-value because of Compton summing of

the annihilation radiation; the bulk of the missing energy is deposited in the DSSSD and will be retrieved in the telescope's total energy reading. Approximately 25 and

40 keV are lost in the P window and the Teflon wrapping respectively; however, these

smaii dead layers are included in GEANT and so this energy loss should be accounted

for in the simulations.

In addition to the slope and offset of the energy calibration, the relative normal-

ization of the 38K and 38mK Monte Carlos and the resohtion of the y spectrum were

aiso free to vary in the fitt. The resolution of the p spectrum was h e d as the function

obtained from the Compton edge analysis (Figure 4.25). The same could not be doue

for the 7 spectrum because the Compton edge ends up being much too sharp. As

mentioned earlier, the lead shielding (and other additional scattering volumes) will cause the 38K background not to be the result of only 2.2 MeV photons, but a dis-

tribution of 7 energies; this will smooth out the Compton edge at Exin = 1.94 MeV.

The resolution of the background was therefore free to grow as large as necessary to

get essentially the same effect and indeed it tended towards rnuch larger resolutions

(typically a:E J JG). This method of smoothing the simulated "K spectrurn

to account for the lack of scattering volumes included in GEANT'S geometry allows the

fit to be extended al1 the way down to threshold, approximately 300 keV as indicated

in the figure (also, see below). The smoothed background is not a perfect approxima-

tion to the true ground state background as is irnmediately evident by the fact that

it extends above 2.2 MeV, the total energy of the initial photon. The calculated 14% contamination from the ground state represents an additional 9 . 4 ~ suppression from the DSSSD analysis scheme (using a AEDsssD 5 laDsssD acceptance) on top of the

35x suppression from the hardware scintillator-DSSSD coincidence. This calculation of the amount of 38K background present in the /3 spectrum can only be considered

approximate, however, because the fitting of the relative normalization is based on the total integral number of counts in the two MCs. This will depend on the shape of the

spectrum and, since it changes rapidly below about 250 keV, is subject to systernatics

which far outweigh the statistical uncertainty quoted.

The imperfect understanding of the -y background is the source of mostt of the dis-

crepancy between the data and the fit, most notably in the 'Valley' at about 450 keV. This compromises the effectiveness of the 511 Compton edge in reducing correlations

between the fit parameters (in particular x,, and X of the scintillator calibration).

The fit of the edge's position in channel number is still good, however, because the

7 spectrum is smooth and does not change very much over the limited range of the

511 Compton edge itself. It wouid be very useful to obtain an experimental shape for

this 38K background because it wouid allow more precise calibrations d o m to lower

energies and provide an overaii better understanding below 2.2 MeV. Attempts were

t.4nother possibiity is an underestimation of the low-energy tail by GEANT, but this d l be shown to be s m d by the results of 84.5.2.

TABLE 4.7: Map of the X2/u as a function of the low-energy cut-off of the fitting region, The threshold determined nom the y sources of 131 chaanels is consistent with this map. The high-energy limit of the fit was fixed at channel 1550.

made to get the shape from events when the 38mK was not trapped, but with only

a 7.6 min haif-life of the ground state, they did not provide nearly enough statistics

in the scintillator-DSSSD coincidence spectnim. A dedicated period of the ne* nin

should be directed towarcis measuring this background, simply by not trapping the

38mK but still having ISAC provide us with the potassium beam.

In fitting the on-line P spectrum, the x2 was found to depend on the fitting region

used, particularly with the low-energy cutoff. This is not surprisingly because the

low-energy part of the spectrum is where the greatest contribution to the x2 cornes

from. In order to have an unbiased estimate of the true energy threshold of the

scintillatort, the threshold was determined from spectra of y sources (88Y, 6 0 C ~ and

13'Cs) which do not contain a 511 Compton edge. These spectra showed that the

threshold does not affect the scintillator's spectrum above channel 131. -4s a check,

the x2 per degree of freedom (v) was mapped as a function of the Iow-energy cut-off

with the results given in Table 4.7. The x2/v as well as the fit parameters can be seen

to change dramaticaliy beiow channel 131, but are ail more or less constant above it

and so this map is consistent with the threshold value found in the y sources. The

threshold is therefore dways taken to be at channel 131 in the scintillator spectnim;

for the calibration of Figure 4.29, this corresponds to 306 keV.

tIt is diff idt to differentiate between the fast fail immediately below the 511 Compton edge and that caused by the threshold.

The dependence on the high-energy cut-off is less sensitive; fits where the upper

limit of the fitting region was varied between 4.94 and 5.46 MeV showed that the

X2/u remained essentially constant: it ody changed by +1.8% at 4.94 MeV, but by

+11.1% at 5.46 MeV. Note that a small background subtraction, not included in the present analysis, would reduce the dependence above the end point; the MC has

virtually no counts above 5.3 MeV, so the X2/u naturally rises due this high-energy

tail (which probably is a result of the cosmic ray background). The fit values for xo

and X (i.e. the calibration) changed only by a negligible amount, f0:$7% and -o,ol 0

respectively. These differences are within the fit parameter uncertainties, so the fit

of the p spectrurn is independent of the hi&-energy cut-off. The counts in the data

are predominantly background above channel 1550 (= 5.2 MeV) and so this value is

chosen for the B fits which follow.

The calibration fit in Figure 4.29 is rather different from that obtained using

the 7 sources (see Figure 4.23 on page 73). The channel numbers corresponding to

5 MeV differ by 2.2%, which is well outside the difference allowved from the calibration

uncertainties. This effect mas bc a result of inefficient light collection from where the

ps generate scintillation light cornpared to the whole; since the ys Compton scatter

hornogeneously t hroughout the plastic, they average over the bulk of the plastic while the ps are concentrated more near the front face of it. Another possibility is the

inaccuracy of GEANT'S ability to properly simulate (à) annihilation-in-flight, (ii) the

differences in the radiative energy losses of e' to that of a Compton scattered e-,

and/or (àia) the relative cross-sections for radiative and collisional energy losses of

positrons. Differences in calibrations from 7 and positron sources has been noted by

others [641, but a full e-xplanation has stili not been found. Since the @ spectrum

fit is to the data themselves and it averages over variations throughout the running

period, this calibration is preferentially used instead of the Compton calibration. The

resolution, however, remains defined by the fits to the Compton edges.

For the p - u correlation experiment, the additional coincidence condition with

the recoil detector virtuaiiy eliminates the 38K Y background and indeed, may one

day be used as a test of the lower p energy part of GEANT'S simulations. At present

though, other uncertainties preclude doing this (see §4.5.2), and so the measurement

on a will be sensitive to how different the 0-teiescope's response function is fiom

GEANT simulations. The present analysis scheme does not, however, use events below

TB = 2.5 MeV; thus the fit of the scintillator's 0 spectrum that is relevant to the

experiment does not include the ground state background. Without fitting the 511

Compton edge, the offset of the calibration cannot be fit, so we fix it to the result

obtained fiom the B fit of Figure 4.29, namely z, c, 42.3 channels. With now only

the slope, A, of the calibration Eree to vary, Figure 4.30 shows the result of a fit

where the low-energy limit of the fitting range was 2.2 MeV. Over this more limited

range, the GEANT simulation of the /3 spectrum is excellent, with a confidence level of

over 80%. This means that for the correlation experiment, GEANT does a very good

job of reproducing the ,!3 spectrum over the region of interest. A potential source

of concern would be a difference in the value of A fit here with that of Figure 4.29,

however the difference of 0.05 ch/hIeV is well within both of their uncertainties.

The two calibrations agree, and this result is important because it shows that the y

background and, to a lesser extent, the DSSSD-GEANT discrepancy, does not bias the scintillator's calibration obtained in fitting the 0 spectrum. The GEANT simulation

of the ground state smoothed with a resolution much worse than measured, is in this

case an adequate approximatian because fitting above it does not change the best-fit

calibration. Therefore, the calibration of Figure 4.29:

c m be considered reliable and should be used in any analysis of the April/May 1999

data set that requires the 0s energy. The differences from the observed DSSSD energy

spectrum and that of GEANT'S may also affect this fit because this energy is subtracted

in both the MC and the data; the calibration may therefore be biased, but only slightly

since the discrepancy is very small compared to the energy deposited in the scintillator.

This effect is addressed later in $4.4.1.

4.4 The Ptelescope

Whereas earlier sections dealt with the E and AE detectors separately, this section

deals with the results hom the April/May 1999 run of the 0-telescope as a whole.

First, the telescope (meaning the T,, + EnsssD = Tp) P spectra are presented and

FIGURE 4.30: Fit of the 3 8 m ~ spectrum above 2.2 bkV to a Monte Carlo simulation. The fitting region (2193 - 5205 keV) is above the 38K background contamination, and so the MC in this case is only of the P spec tm. The offset of the calibration is fixeci at xo c, 42.3 from Figure 4.29 because the 511 Compton edge is not fit.

discussed. FoHlowing this is i4.4.2 which compares backscatter calculations of GEANT to those on-line using the DSSSD position information. The uniformity of the tele-

scope response to the incident positron's direction is discussed in i4.4.3. The final

section explains how the P-telescope may be used to measure be, the Fierz interference

parameter.

4.4.1 Total P Energy

The previous two sections have provided us with both the calibration and the resolu-

tion of the scintillator and al1 of the brty-eight DSSSD strips, as well as an effective

position decoding analysis scheme. The calibrations allow us to sum up the scintillator

and DSSSD energy readings for a total Tp measurementf. Having an understanding of these detector resolutions further allows us to program GEANT to simulate the

telescopels B spectrum of the 38mK decay; the resolutions are essential because they

must be applied before adding the two energies (as is the case with the real data)

rather than Btting them after, Prior to fitting or comparing the on-line spectra to these MCs, considerable effort must be made to ensure that al1 conditions placed on

the on-line data are reflected in the simulation. As a quick list, the most important parameters to consider are:

The detectors' resolutions and calibrations (fixeci).

1 The scintilIator's low-energy threshold (user parameter).

a The DSSSD low- and high-energy thresholds (user parameters).

The active area of the DSSSD (user's choice; for example, whether or not the

edge strips are included).

We saw earlier in Figure 4.28 how the value of ocut used in the analysis of the

on-line data has an impact on the resul ting P- telescope's spec tra. The correspondhg

figure for the total energy, TB = Tsin + EDsssDl is given in Figure 4.31. -4 qualitative

cornparison of these two figures tells us that the additional low-energy events in the

fact, this coupled with the position information gives us a rneasurement of the positron's momentum, p,.

- al1 accepted ps

-

O 1 2 3 4 5 6

T, [MeVI

FIGURE 4.31: The telescope's ,û spectra for different AEDsss~ conditions. These are the corresponding spectra for Figure 4.28; they have the sarne conditions applied and ody ciiffer in that the DSSSD energy has been added to the scintillator's.

larger AEDsssD spectra are not due to the greater acceptance of high-energy DSSSD events (as suggested they may be in 843.5) because adding back the DSSSD energy

does not remove this low-energy tail. With just a Little imagination, one can see the

Compton edge of the 2.2 MeV background in the 3aDsssD 0 spectrum, indicating

that the larger acceptance instead allows a greater contamination from this, and

presumably other, backgrounds. Thus unless statistics is a great concernt , the tighter

AEDsssD energy cut of < ~ u D ~ ~ ~ ~ should definitely be used.

The Compton edge at 340 keV, prominent in the scintillator's energy spectrum,

no longer appears once the DSSSD energy has been added back in. If the peak

remainecl, it would indicate that these events fired just above the DSSSD's threshold,

and they would likely be due to a random fluctuation above threshold, randomly

coincident low-energy photons, or they might point to a flaw in the analysis scheme.

The fact that the edge does not remain in the telescope's 0 spectrum shows that an

appreciable amount of energy was deposited in the DSSSD; this is consistent with a

tWhich may be the case once the recoil coincidence is applied, for example.

positron scattering or stopping in the strip detector, and then one of the annihilation

quanta Compton scattering in the scintillator. The total energy of these events are

distributeà above the Compton edge in the ,O spectrum, so the telescope wàll contain

some background from these events, but these events are ( i ) impossible to remove

by a re-design of the telescope, (ii) a smali percentage of the total number of events,

and (iz'i) reproduced reasonably well by GEANT for the scintillator's spectrurn as

shown in Figure 4.29. They can be greatly suppressed, however, simply by setting the scintillator's (software) threshold at or above 400 keV in the analyzing program.

Although it is good that these events do not remain a well-defiaed Compton edge in the telescope's spectrum, it also perhaps a little unfortunate because we no longer

have two distinct points to fit to as before. As was the case when fitting above

the 2.2 MeV background, we must fix the offset of the energy calibration. For the

telescope, this 'energy calibration' will be different from the scintillator or DSSSDYs

in that it is alreadg calibrated, and therefore in units of energy rather than channels.

If we were to fit the MC to the telescope's 0 spectrum and if everything was perfectly

calibrated and simulated, the telescope's calibration:

would yield an offset of T; = O keV and q = 1 keV/keV for the slope. The poor

agreement between the DSSSD's energy spectrum and that simulated by GEANT is an

immediate indication that this is not the case. To first order, however, the difference

between the DSSSD and GEANT'S energy distributions is given by the difference of

their mean dues , which is -10.3 keV (see Figure 4.18). We therefore can account

for the AE's discrepancy on auemge by fixing the offset to be f10.3 keV.

The spectrum from the on-line data and the results of a fit to a MC simulation

is given in Figure 4.32. As mentioned earlier, the resolution of the detectors must

be input into the MC before adding the detectors' energies up, and therefore the

resolution cannot be fit. The free parameters in this fit are just the dope of the

calibration and the relative normalization of the P and 2.2 MeV y background. The

simulation of the ground state, which is convolutecl with the same resolution as in

Figure 4.29, is not as good an appravimation anymore as the Compton edge is clearly

visible at 1.9 MeV. The unreasonably large resolution of the ground state in fact

q = l.ûûûiû(t5) keV/keV x2/v = 2.3097 C.L. = O

FIGURE 4.32: Fit of the 38mK Tg spectrum to a Monte Car10 simulation. The offset was fixed at 10.3 keV because of the average ciifference between the GEANT sirnu- lated and measured DSSSD energy spectra. The 38K background is not reproduced as weU when the DSSSD energy is added back in.

can be seen to limit our low-energy fitting range because it unphysicaliy places events

belorv the scintillator's threshold, resulting in a low-energy tail. One point that should

be noted is that the resohtion of the 38K background in the DSSSD was not adjusted

since we bave no idea what the DSSSD's spectrum is in this case. Indeed, simulations

indicate a higher average energy ioss than the 38mK OS, and since there already is a

DSSSD-GEANT discrepancy, the DSSSD's 38K spectrum can play a more important

rote. Perhaps most significant, however, is the fact that in this case the background

shape in both detectors must be Gxed when fitting the P spectrum, rather than open to

approxhating over-estimations of the resolution. It is not too surprising, then, t hat

this total fl energy spectnim is not reproduced as well. Once again, an experimentalIy

measured spectrum shape for the p u n d state is essential for a good understanding

below 2 MeV.

FIGURE 4.33: Fit of the 38mK TP spectrum above 2.3 MeV to a Monte Car10 simulation. Above the 38K background, the MC is seen to reproduce the on-line 3SmK p spectrum very WU.

The fit to the data naturally has a large X2/u due to the ground state background,

but otherwise the fit looks very good. The fit to the re-cdibrated dope is unity within

uncertainties which is encouraging. As with the scintillator's spectrum, we aiso fit

above this ground state to see how that affects the calibration. The resdt is piotted

in Figure 4.33 and again we find that the MC does an excellent job of reproducing the

data. The fits were sensitive to the low-energy cut of the fitting region, and aeeded

to be pIaced siightly hijher than expected (5 2.2 MeV) in order to obtoin good

agreement. The value of 71 is one to within 0.06%, which is a dear indication that the

DSSSD-GEA~VT discrepancy is negligible once the average ciifference is accounted for (TB = 10.3 keV) .

4.4.2 Backscattering Losses

As discussed earlier, one of the reasons TRINAT decided to switch to a plastic scintil-

lator instead of the Si(Li) as the E detector was to reduce backscattering losses. The

low-Z plastic has a relatively low probability for backscattering and the simulations

of Figure 4.2 indicate that Our losses are dominated by backscattering off the DSSSD; this represents an overall loss of event acceptance and can affect the p spectrum if

an annihilation photon then Compton scatters in the scintillator, as discussed in the

previous section.

There is also another type of backscattering loss to consider, and one that can

be measured and then compared to GEANT as a check of how well it is reproduced

in the simulations. Consider events where the ,û first goes through the DSSSD, then

scatters in the scintillator, and eventually scatters back out through the DSSSD again.

These events (hereafter called 'backscattered events') will add to the low-energy tail

of t he telescope's response function because energy is deposited in both the E and AE detectors. The pixel of the DSSSD that the positron enters through will, in general,

differ from the one that it backscatters out through; in this case, the event is flagged

as a double hit and vetoed by the analysis of the DSSSD position information. Vie

assume that these double hits in the DSSSD, where both ( 2 and i ) group hits passed

the position and energy cuts (ucut = 1) of the DSSSD analysis scheme, are primarily a

result of this backscattering effect; the probability of a random double P coincidence

is very smaii considering our P event rate of typically 5 30 Hz. The fraction of these

backscattered events in the 38mK data was 1,12% of the total number of accepted ,û (one DSSSD hit) events using ucut = 1 in the analysis scheme. If the DSSSD energy

agreement is increased to uot = 3, the fraction of backscattered ,û9s increases to

1.35%. In either case, events where there was more than two groups in 2 or @ were

still excluded (les than 0.09%), and not considered to be a backscattered P. GEANT simulations can also have these backscattered events tagged, and the cornparison to

the on-line data gives an idea as to how well GEANT calculates scattering within the

scintillator. The result of a simulation of the unweighted B spectrum was 1.22%. This

is in agreement with the data, considering the spread in the results fiom the choice

of G u t -

4.4.3 Uniformity of Response

The gain of the scintillator may Vary according to where in the plastic the scintillation

light was generated because the light collection efficiency can vary with position. Off- line tests were performed with a *07Bi source where the source was moved along the

length of the scintillator, with variations in the gain found to be at the 1% level.

This preliminary result is encouraging, but the effect on the correlation expriment

can be different. By placing different position conditions on events in the DSSSD, Ive

can use the on-line 38mK data to map out the non-uniformity. The difference in the

B spectra of the different cuts can be used to determine our sensitivity. For example,

if we define an 'inner' DSSSD position cut and and outer DSSSD cut, we cm check

that the light collection of the scintillator around the centre is the same as near its edge. In order to obtain good statistics on the /3 spectra, a large area at the centre

of the DSSSD (defined by a 01.2 cm circle) was chosen for the inner cut; an outer

area defined by strip positions outside the 02.4 cm circle has the same area as the

inner circle. Circles are defined (rather than 0.1 mm \ide squares) because of possible

inter-strip events, even though they are but a small fraction of the the single-strip

events. Note that these circles do in fact have an equal number of the dominant

single-strip pixels (only one strip in 2 and one in e). The /3 spectra of Figure 4.34 are the results where the inner and outer position

conditions were imposed on the 38mK data set. The outer DSSSD events' efficiency is

83% that of the inner ones and this is mainly due to the reduced efficiency of the edge

strips as discussed in i4.2.5. In order to aid in comparison of the spectra, this relative

inefficiency has been corrected for by renormalizing the inner DSSSD's spectrum to

have an equal number of counts as the outer. The plot in the upper right of the figure

is the difference in the number of counts, and generally the agreement c m be seen to

be very good. The difference is < f 5% in the number of counts (For energies less than

4 MeV; see plot in upper right of Figure 4.34) indicating uniformity of the scintillator

and telescope as a whole to the direction of the incident P. Above 4 MeV, the difference 2Q a considerable fraction of the total number oicounts

and we should determine how sensitive our measurement of the correlation parameter,

a, wi i i be to this non-uniformity. To that end, full Monte Car10 (651 simulations with

FIGURE 4.34: Uniformity of response of the plastic scintillator. The two ,O spectra ciiffer by the position condition of the DSSSD imposed on them: the shaded 01.2 cm circle in the ceutre (%mer') and the shaded area of the corners ('outer') chosen such that the two have equal DSSSD areas. The plot insert in the upper right is the (percentage) difference in the nuniber of counts between the two spectra.

both responses must be performed. The resulting fits of a to t hese fake data, and

their deviations from that input into the MC, will give us the relative importance of

the telescope's uniformity.

4.4.4 The Fierz Interference Term

The Fierz interference term, b,, of Equation (2.24) will, in general, be non-zero if

a # +l; this is made explicit by Adelberger, et. al [IO) when they express their mea-

surement in terms of à r i+be(ze,Ee). The final analysis of TRINAT'S ,û - v cor-

relation experiment may very well incorporate 6, by directly fitting the CS,V and

C$,v parameters; in the present analysis scheme, our sensitivity to this interfer-

ence term will be small because it only considers events above Ep = 2.5 MeV where

0.093 < mJE, < 0.17. With the limit of Ibe( 5 0.007 1111, the impact on the correla-

tion parameter is relatively mail: ü would only differ from a at the 0.1% level.

The abity to reproduce so well the unweighted B spectrum for the 38mK data

aliows us to consider fitting be using the telescope on its own. A preliminary investi-

gation into this prospect has been completed which looks very promising, but a more

detailed analysis is necessary to compete with current limits. The unweighted P spectrum was fit to MC simulations as in i4.3.5, but this time the number of counts in

this MC spectrum was renormalized

and Wyld's Coulomb correction):

Ni,c(E)

by (see Equation (2.24) with Jackson, Trieman

where be was a free parameter in the fit. The other parameters left free to vary

were the slope of the energy caiibration (A of Equation (4.10)) as well as the relative

normalization and resolution of the 38K background (which \vas not renorrnalized by

Equation (4.19)). The slope of the calibration in t his fit agreed with the fit when b, was set to zero: X = 289.59 f 0.13 versus 289.72 f 0.15 channels/MeV and xo = 4Z2 f 0.4

versus 42.3 f 0.4 channels). This is an important result because it shows that the Fierz interference term will not bias our on-line p calibrations of the scintillator.

The normalization of the y background did significantly change, however, and was

highly correlated with 6, (97%). This is a result of the poor spectmm shape of

the background simulated by GEANT, and limits our sensitivity to be since energies

below the Compton edge are where the interference term will have the largest effect.

The result of this fit was 6, = -0.05 & 0.03 which is much larger than the limit of

Ibe[ 5 0.007 f 0.005 [Ill reported earlier. If only A of the calibration and b, are left free (with the background fixed to the results of the fit with 6, = O), then the limit

on b, is very good and comparable to the published results: be = -0.003 k 0.008. There is no justifiable reason for Luing the background parameters, however, and this rcsult is only an indication of what limits may be attainable once efforts in

understanding the shape of the 38K background are cornplete; in addition, questions

about non-linearities in the scintillator gain will need to be addressed, and calculable

higher-order corrections must also be included.

4.5 P A r Coincidences

The MCP-@-telescope coincidence spectra are presented in this section. As this is

largely the basis of A. Gorelov's thesis [la], the analysis contained here is preliminary

and only meant to give an indication as to how the /3-telescope will be used (as well

as how it will perform) in the ,8 - v correlation experiment. The k t section explains

the scattering effects that are present in our geometry and shows how well GEANT reproduces them. The other section compares simulations of 0 spectra where a recoil

coincidence is required to those observed on-line in April/Way 1999.

4.5.1 Scattering Effects

The plot in Figure 4.35 is a Monte Carlo simulation of the 0-v correlation experiment

for the Ar" recoils. This MC is a combination of GEANT (positron tracking) and

A. Gorelov's (recoil tracking) code [651. The electric field of -829 V/cm is not strong

enough to collect all of these recoils, but it does increase the eficiency greatly and is

easily implemented in the analysis if it can be considered uniform, as it was in the

simulation. The efficiency of the MCP is assumed to be uniform, and its active area

has been assumed to be 02.5 cm. The kinematic limits indicated in the figure were

calculateci for the back-to-back geometry using point-like detectors wit h an ideal 0 response function. The Monte Carlo includes the finite trap and detector sizes, as

well as the energy and timing resolution of the @-telescope; the Compton summing of the annihilation radiation is clearly evident as a cidge at P energies above the slow

branch.

The events outside the kinematically allowed region at longer times-of-0ight de-

serve special attention because they correspond to positrons which were not emitted

toward the D-telescope, but (predominantly back-) scattered before entering; this will

bias the initial direction of the recoil and hence the TOF. Consider the case where

the At' ion recoils toward the B detector; the electric field is strong enough t hat it

will be tunieci back and accelerated onto the MCP. If the decay is in the fast branch

of this 'reverseci geometry', then the recoil TOF dl be constant (at N 1 ps) and

the leptons will both be emitted toward the recoil detector. The positron then has a non-negligible probability of backscattering off the MCP (lead glas) or one of its

electrostatic hoops (aluminum) into the ,8-telescope. If this happens, the event would

be detected just Like a 'good' ,8 - Ar coincidence, but outside the kinematic limits at

longer TOF. These events are plotted separately in the bottom of Figure 4.35- Now

FIGURE 4.35: Monte Carlo simulation of the recoil TOF as function of P energy for ~ r + ' recoils (top) with the kinematic ümits for the back-to-back geometry (solid lines), Events in the kinematicaily forbidden region at longer times-of-Elight are a result of positrons that scattered before firing the Ptelescope. Most of these events are a result of the p backscattering off the recoil detector or one of the electrostatic hoops (bottom).

n

a 900 - Y

Er. eoo - '

H .I

O 700

Q) L

=-., . . x. . . . . . . '. : . \., . . . . .

1. :.: \ '

. . . . . . ? .,;. . . . . . . . . . . . ..:. . . . . . . . . ....... ::..\ ...... .......... : :Y,.

- : : : : : : ; : : : : . ; : ::::::::>-.' ............ ..\.. ....................... . v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................. -5' ................................. s,. . ..................................... -

-

500 1 , , 1 r O 1 2 3 4 5 6

T, (MeV1

-

*

1100 -'

1000 -. - 2 9oo Y

kt

800 - e .d

& 700 - L

600

I , t I

backscattered off MCP or hoop

.,:: .i:ii*#yjijli;;ii;ii:i:i - .*- .:.: i: : .................... .t..:'....*....... . . . . . . . . ........ . . ............. :'::' - : .............. . . - ' . - . ........ . . . . . . . . . . . . . . . . . ...... ....... . . . - . . ..y..- ........ . - . - . <..: . . . . . . . . . . . . . . . . . . . 7 * * . . - : . y - . . . . * . . . ..

',

--.... . -- . . . . A ., ... . . -. .

-& ... :. .... - .

consider a backscatteredt /3 which came from the slow branch; the recoil in tbis case

is directed toward the recoil detector rather than away, and so the event is detected

at faster TOF. Essentialiy, the s p e c t m shape of the backscattered ,f3s will have the

same form as the 'direct' ones, but it is reversed in TOF and shifted down in /3 energy

(from the energy lost in the volume where it backscattered).

The events where positrons backscattered off the MCP or one of the hoops were

tagged in the Monte Car10 once it was found to be a clearly visible background.

Table 4.8 gives the percentage of /3-Ar coincidences where the positron scattered off

a volume before firing the telescope. The G10 frame of the DSSSD and the inside

part of the front face of the telescope vacuum chamber that defines the /3 window are

seen to scatter the largest fraction of the events. Exclusion of the edge strips does not

reduce these scattered events as much as one might expect; t his agrees with the lack of

(real) low-energy tails observed in the edge strips, although other systematic effects

still favour restricting the DSSSD active area. The major concern regarding these

events is that though they will appear to be good /3 events, they will be registered in

the wrong DSSSD position (and so will yield an incorrect measurement of Bpv) and will be in the low-energy tail due to the energy lost when scattering. The MCP and

electrostatic hoops are the dominant source of backscattered 0 events and explain

most of the background seen above the slow branch in TOF; additional volumes off

which the B can backscatter include the rnount for the hoops behind the MCP, the

MW's flange and the vacuum chamber itself.

We do in fact see evidence of these backscattered Bs in the on-line data, rvhich is given in Figure 4.36. -4 comparison of this with the simulation of Figure 4.35 shows

that the two are very similar and that the MC does a good job of reproducing the scat-

tered events. The two differences between them are a srna11 constant background from

random MCP-telescope coincidences, and the tail of AP2 events at TOF 5 550 ns.

The TOF for the fast branch of the backscattered events of the Ar+* will overlap the

(direct) fast branch of the Ar*'. This same effect will occur for a11 higher, otherwise

resolved, charge states as weU. Once a EB cut of 2.5 MeV is applied, however, the

backscattered peak is greatly reduced, and the different charge states are separated

+This definition of 'backscatter' is not the same as in 84-42; in this case, it cornesponds to positrons that were initiaüy ernitted in the -2 direction.

p scatterhg volume / @ Ar" h+2 h i 3 h + 4

Steel around 0 window

- including edge strips - excluding edge strips

- excluding edge strips / 1.32% 1.65% 1.85% 2.02% 2.02%

1.85% 2.59% 2.69% 2.73% 2.72% 1.73% 2.27% 2.47% 2.48% 2.42%

G10 DSSSD mounting - including edge strips 1.42% 2.03% 2.28% 2.45% 2.55%

Lead glassofMCP (including edge strips)

TABLE 4.8: GEANT calculations of the percentage of 0s that scatter before firing the telescope for various Ar recoil charge States.

0.28% 0.12% 0.17% 0.19% 0.20%

hoop (including edge strips)

in TOF so that this is not a serious concern.

-4 measure of the quality of the GEANT simulations can be estimated by comparing

the TOF projections of Figures 4.35 and 4.36. Such a comparison for the ArfL recoils

is given in Figure 4.37 where the background was fit to the events between the Ar+' and Ar0 peaks, and the fit cuve (Monte Car10 + background) is normalized to have

the same number of counts as the on-line data. The MCP positioning is not fully

understood at the present time, and known non-uniformities in the electric field of

the April/May 1999 data are not included in this preliminary analysis. However, once

they are, the comparison over the peak of the fast branch should improve greatly. The

backscatter peak is nut quite as large as in the data, but the MC does account for

most of it; the addition of the ceramic rods used to mount the electrostatic rings into

GEANT'S geometry should reduce this difference even furthet ir. future simulations

that include them.

Regardless of the outcome as to GEANT'S reliabityin its absolute scattering rates

once a detaiIed anaiysis is completed, it has already helped improve the experiment

0.48% 0.78% 1.00% 1.23% 1.44%

FIGURE 4.36: Scatter plot of recoil TOF versus Tg Crom the on-iine 38mK measurement. The sarne kinernatic limits as in Figure 4.35 are plotted for comparison.

FIGURE 4.37: TOF projections for the and comparison to GEANT. The solid line represents the full GEANT simuiation and the i Iast I I . ( i line are events where the positron backscattered off of the hiCP or one of its electrostatic components before entering the Ptelescope.

L

- i '

-

4 1 I 1

10' - CEANT simulation - ..

***.

- - scattered off MCP or hoop .-. -- - - constant background . *-.. . 1

102 ;

IO' ! -

loO

10' I 'Z I

. * , * '

- a 1 '1

4 l

1 i

I i 1.- ._ ------- ..-------z-=-- -------- t t

400 600 800 1000 1200 1400 Time-of -f light [ns]

by identifying the backscatter background and, once known, its TOF bas proven to be useful in understanding the electric field.

4.5.2 3 8 m ~ /3 - Ar Coincidence Spectra

Although not easily evident in the scatter plots of the previous section, the @Ar coincidence condition virtually eliminates the 38K background. This can be clearly

seen by the examining the recoil-coincident ,LI spectra and looking for any sort of bump

at around 1.9 MeV. Using the same analysis as was done for the ,ü spectra in i4.3.5

and i4.4.1, these spectra are given in Figure 4.38 for the different recoil charge States

Ara, ArL and A3; the Ar3 and Ar4 are continued in Figure 4.39. Both the scintillator

(left) and the scintillator + DSSSD spectra (right) are comparedt to MCs. Happily, there is no evidence of a 38K background in any of the spectra; this result

is expected because the probability of the y firing al1 three detectors is &remely

small. In fact, the MCs generally agree very well with data for Txin x T', < 2 MeV. It is for this reason the claim was made (see page 83) that the discrepancy in the

scintillator's /3 spectrum was predorninantly due to the 38K background, and not from

a grossly incorrect GEANT simulation of the low-energy tail. Note in particular how

GEANT correctly reproduces the Compton edge from the 511 keV annihilation quanta

in the scintillator spectra; this indicates that the discrepancy in Figure 4.29 is due

predominantly to the misunderstood 38K background, and not GEANT'S simulation of the background.

We can actually hope to one day test the low-energy tail of GEALW'S response

function by seeing how well it reproduces the data of these background-free spectra.

At present, however, the data are subject to a number of uncertainties:

0 The MCP efficiency. This is most notably true for the ,4r0 because their ef-

ficiency is unknown and may vary significantly. The charged recoils are al1

accelerated to energies where the response is flat to within 2%.

0 The electric field. Considerable effort has been made to understand the electric

field as thoroughly as possible [57j, but the preliminary analysis presented here

+Note, they are not, in any way, fitted; the relative normalization is chosen so the data and MCs have an quai number of counts.

FIGURE 4.38: The 38mK P spectra coincident with @, Ar+' and .Ar+Z recoils. Overlayed is a Monte Carlo simulation which assumes a uniforni MCP efüciency and a uniform electric field of -829 V/cm. The caiibration was taken from the fit of the unweighted @ spectm, Figure 4.29 on page 82.

F~GURE 4.39: The 3 8 m ~ P spectra coincident with and Ar'' recoils and cornparison to Monte Carlo simulations.

bas not incorporateci k n m non-uniformities. indications are that the tield was

dose to -829 V/cm near the trap, but decreased to about -780 V/cm at the

surface of the MCP.

The active area of the MCP. The position spectrum of the MCP is not Fuily

characterized yet and this affects the present àiscussion because, althougti we

are integrating over the whole area, we need to accurately know what that

area is. It was faund that by changing the MCP radius by 1 mm the resulting

spectra were noticeably different, especially for the neutrals and lower (< 3)

charge states.

Considering these varied systematics, the present comparison of GEANT to the

on-line data must remain relatively qualitative. The different charge states were

chosen by simple cuts in TOF; a more detailed analysis should corisider the overlap

of higher charge states. To iudicate the differences that currently exist, tables of the

first through third moments of the two spectra are given in each plot of Figures 4.38

and 4.39. The differences are largest for the Ar0 data which is most likely a result of the MCP eEciency. Aii of the charged recoils have better agreement which is expected

since the uncertainties in the electric field are less than the uncertainty in the efficiency

of the neutrals. As we go to higher charge states, the coincident-P spectra look more

and more like unweighted /3 spectra and the agreement generally improves.

Once the systematics are better understood, a detailed analysis of the recoil- coincident B spectra may be made. This would complement fitting the ,&singles

spectrum down to threshold once the shape of 38K ground state background has been

meaured.

Conclusions

A j3-telescope consisting of a double-sided silicon-strip detector and a plastic scintit

lator has b e n designed and constructed ta observe the positrons emitted in the P decay of 38mK.

The energy calibration of the plastic scintillator has been accomplished using the

Compton dges of various y sources as well as by titting the on-line P spectrum to

detailed Monte Car10 simulations. The resolution of the scintillator is derived from

the Compton edge analysis and found to foUow the square-mot law expected if it

is dominated by scintillation photon statistics. The width, ust of the scintillator's

timing resolution relative to a micro-channel plate detector bas been measured to be

one nanosecond. These characteristics fuifill, and in some cases even surpass, the

specifications we had set wben designing the scintillator.

The calibration and resolution of each strip of the A E detector have also been

determined by using both low-energy photon sources as well as the on-line data

themselves. The strip detector is an essential cornponent of the 0-telescope because,

in addition to providing the position information needed for a measurement of the

positron's momentum, it is an effective tag for ,û events and greatly reduces y back-

grounds.

Monte Car10 simulations using GEANT are generally in good agreement Nith the

measurements of TRINAT'S April/May 1999 38mK data set for observables that are

independent of any scalar interactions which will be determined in the final analysis.

There is a (EDsssD) = 10.3 keV diirepancy between the MC and the measured en-

ergy spectrum in the strip detector that is not presently understood, but the impact

on the total Tg measurement was found to be negligible. The sirnuiations reproduce

CHAPTER 5 CONCLUSIONS 107

the scintiUator7s B spectra very well, although our understanding below 2.2 MeV is

complicated by the large 38K (ground state) y background. The E - AE coincidence

reduces this background by more than 99.5%, but there is still about a 15% contam-

ination in the telescope's 0 spectrum. GEANT colculations of the fraction of /3s that

backscatter out of the plastic and through the strip detector a second time are in

agreement with those found in the data.

The goal of TRINAT'S 38mK B decay experiment is to make a precise measurement

of the 0 - u correlation parameter a. The P-telescope's most significant contribution

to the uncertainty in this measurement, a,, is 0.05% taken from the uncertainty in

the 0 calibration of the scintillator; possible non-linearities in the gain may increase

this uncertainty to 0.5%. The uniformity of the scintillator's response over the active area of the strip detector has been investigated, and small differences are noticed.

This is a concern because it will be highly correlated with Op,, but an estirnate of the contribution to a, still needs to be performed. The ground state's y background,

prevalent in the telescope's unweighted @ spectra, is virtually eliminated once a recoil

is required to have fired the micro-channel plate detector. These Ar-coincident P spectra have been compared to preliminary MC simulations and though the spectra

are reproduced reasonably well, further detailed analysis will improve the agreement;

in particular, understanding the active area of the micro-channel plate and proper

inclusion of the non-uniform electric field are necessary for the a measurement.

The data set from April/May 1999 has enough statistics for a 0.3% measurement

of a, but the final analysis is still in progress. Continued experiments are planned with

an improved geometry for a cleaner measurement wit h bet ter statistics. Alt hough the

energy and timing measurements of the positron in this data set are precise enough

considering the statistics accumulated, further improvement in our understanding of

the P-telescope is of course desirable, and below we outline how this rnay be accom-

plished.

The greatest advancement may be made by experimentally determining the shape

of the 38K background and by reducing the amount of this background relative to

the 38mK B spectrum. According to GEANT simulations, the plastic scintillator is

much larger than is necessary for the experiment; by simply making the scintillator

half the current length, we should be able to reduce this background by a factor

CHAPTER 5 CONCLUSIONS 108

of two. The shape of this background c m easily be determineci in TRINAT'S next

experiment by accepting ISAC'S potassium beam but not trapping the isomer; we can

then measure the spectra of just the ground state where both the E and Al3 detectors

fire. Such a determination would aid in calibrating the scintillator and is essential if

the unweighted @ spectrurn is to be used to measure the Fierz interference parameter,

be The need for the large corrections in the extended calibration of the strip de-

tector may be reduced with a better initial calibration of the strips, particiilarly if

this calibration covers more of the experiment's energy range. Calibrations using an

open electron conversion source would complement the low-energy photon sources and

may help to explain the small discrepancy between GEANT'S simulation of the strip

detector's spectnim with that observed in the data.

Possible non-linearities in the scintillator's energy calibration should be investi-

gated further using y sources over the energy range 2 - 4 MeV. Additionally, ex-

tending the Compton edge calibration to higher energies may reduce the differences

observed in the 7 and P calibrations of the scintillator.

Although GEANT seems to reproduce the experiment very well, a complete un-

derstanding of the telescope's response function can only be made using a well char-

acterized beam of mon~energetic positrons. Such a study could be undertaken at

a dedicated facility such as the pelletron facility at the Mau Planck Institute at

Stuttgart [661, or at TRIUMF as has previously been done [401. The appeai of Stut tgart

is the excellent beam quality whereas doing it locally would allow us more time to

optimize the set-up and reproduce the environment of the correlation experiment as

closely as possible.

Response funct ion of the scint illator

Ideally7 the signal generated by the scintillator, XADC, is a perfect representation of

the energy deposited in it, Tsin, In reaiity, every detector has a response function

which relates the actual energy deposited and the resulting observed signal. Typical

response functions (shown in Figure 4.1) have a large peak corresponding to the incident particle's kinetic energy as well as a low-energy tail where part of the energy

loss wvas undetected. The positron response function has an additional high-energy

tail due to the finite probability of detecting the annihilation radiation as well.

To understand the characteristics of the response, we need to understand the pro-

cess by which the particle is detected. The incident particle interacts with the scin-

tillator and suffers energy loss through Coulomb interactions with atomic electrons.

These electrons are then excited to a higher energy level in the atom (excitation) or,

if the energy transferred is greater than the binding energy, is ejected into the contin-

uum. In the latter case, these freed atomic electrons (which are known as 6 rays) suffer

energy losses and excite other atoms as they transverse the scintillator, just like the

primary particle. The atoms in the excited states rapidly decay to the ground state

by fluorescing, which is to say they emit (visible) photons. Some of these photons

are collected on the photosensitive surface of an optically coupled photo-multiplier

tube (PMT), ejecting (at most) one photoelectron per photon. These photoelectrons

are accelerated and focused by electrodes called dynodes, which are typically made

of materials with a high secondary electron emission probability so that the cascade

is multiplied as well. The resulting pulse after repeated amplification through the

dynode structure of the PMT, is the h a 1 signal generated by the scintillator.

Saturation Effects

The efficiency of the excitation process is not unity and in fact is dependent on the

local energy los. Since there are a 6nite number of atoms near the ionizing particle,

it is ceasonable to expect that as the dE/dx gets large, the efficiency is reducecl as

there are fewer atoms nearby that are still in the ground state. This saturation effect

was first investigated semi-empirically by Birks [671 who parameterized the amount

of scintillation light generated (luminescence) in terms of the energy loss:

with A a proportionality constant, p the density of the medium and kB is a factor

which Birks found to depend primarily on the type of particle. The number of scin-

tillation photons generated is proportional to the integral of Equation (A.1) over the

range of the particle's track. In the limit that < t, the scintillation light gen-

erated 2s proportional to the energy lost, and saturation only becomes important for

large dE/dx. For Compton electrons and P's, ks = (9 - 10) x 10-~ k e ~ " ' cm-2, so that dL/dx a dE/dx to within half a percent below energy losses of about 5 MeV/cm.

If the incident positron has energies greater than about 100 keV, the energy loss

will be relatively Bat at about dE/& 2 1 l\kV/cm (see Figure Al). These positrons

will only be slightly modified by the saturation effects. The energy loss of positrons

below 100 keV is larger; in this case, the Birks effect can become significant and may

affect the arnount of scintillation Light generated. As this is well below the scintillator's

threshold, we do not need to worry about these low-energy effects for the correlation

experiment . This quenching effect, however, not only occurs for the primary particle, but also

to any generated secondaries, such as b rays. The positrons in the energy range of

interest to the experiment may not be heavily affected by saturation, but it is difficult

to predict how large the dE/dx of the generated secondaries wili be, To estimate t bis

effect, GEANT simulations were performed where the Birks factor was included in the

scintillator's response. The value used was kB = 10 x 10-"ke~-~cm-* and the

results are given in Figure A 2 This is a scatter plot of the initial p's kinetic energy

against the energy lost to saturation effects, whether from the initial positron or a

FICURE Al: Total cross-sections used in GEANT for the energy loss of positrons in plastic. The dominant interaction is Bhabha (e+e- -P e+e-) scattering which generally generates 6 rays, but brernsstrahlung (e+ -. yef) and even annihiiation- in-ûight (e+e- + 27) contribute.

- O 1000 2000 3000 4000 5000

Energy deposited in scintillator [keV]

FIGURE A.2: Monte Carlo simulation of saturation effects in plastic with ks = 10 x 10'~ k e ~ " cm-2. The solid line represents the energy loss expected using Equatian (A-l), but the effect is siightly enhanced due to the production of 6 rays in the GEANT simulation.

secondary. The solid line is a calculation based on tables of the dE/dx for positrons in

NE104 plastic (only the primary positron is considered) and Equation A.1. As both

the Birks effect and 6 ray production are inherently random processes, we expect to

see the spread in the energy lost to quenching as seen in the figure. Note that for

higher /3 energies, the average energy lost is not equal to the calculation; this is due

to the higher production of d rays which, since they are lower energy electrons, suffer

more saturation than expected if no 6 rays were produced.

The Monte Carlo simulation shows that this is a relatively small effect (< 2%) and

furthemore that it is nearly linear with energy. The quenching therefore manifests

itself simply as a slight change in the slope of the energy calibration, allowing us to

neglect the efféct and assume that the light output is proportional to the energy deposited. The spread depicted in Figure A.2 indicates that, by making this assumption

and calibrating to the average light output for a given positron energy, for any given

event we have about a f 20 keV uncertainty in the energy reading as a result of satu-

ration effects. This is not important for the correlation expeciment where we do aot

plan to utilize the event-by-event information, but analysis which incIudes kinematic

reconstructions (se, for example, jB.2) should make sure that this is considered.

Bremsstrahlung

The low-energy tail of the response functions arise mainly from three effects: (a')

particles (primary or secondary) that escape the scintiilator and therefore do not

deposit al1 of their energy, (za) radiative energy losses (bremsstrahlung) that escape

detection and (iài) annihilation-in-fiight quanta which take some of ef's kinetic energy

out of the detector. The first is brought up within chapter 4 (design simulations and

backscattering losses from the plastic) and the third is discussed in 5A.3; below we

briefly discuss bremsstrahlung losses. Often as an electron or positron is suffering collisional losses within the detector,

its velocity quickly changes when it scatters into large angles, which is enhanced due

to their small mas. This results in drastic decelerations and since any accelerat-

ing charged particle must radiate electromagnetic energy, the e* lose energy through

bremsstrahlung photons (instead of ionization losses). If these photons escape the de-

tector instead of being re-absorbed and generated into scintillation light, the detected

energy will be les than the incident particle's, thereby adding to the low-energy tail.

In the relativistic limit, which is where radiative losses contribute significantly, the

ratio of ionizing energy losses to that of bremsstrahlung for electrons is given by 1681:

For scintillators, the 2 z 5.6 so that at Te 5 5 MeV, this ratio is less than 4% (see

Figure A.3). In cornparison, this ratio is 10% for a higher Z material detector, for

example a Si(Li) for which 2 = 14, . The ratio increases because the electrons are

more likely to scatter into large angles; thus the Si(Li) bas a larger low-energy tail in its response function than the lighter scintillatort. This was one of the motivating

reasons for switching £rom a Si(Li) detector to the plastic scintiilator described in t his

thesis.

tAlso contributing ta the %(Li) low-energy tail are e* that backscatter out of the detector before stopping; this is also a fimction of the detector's 2.

-e- Be408 - f - silicon - 8- silicon k

FIGURE A.3: Radiative energy losses in plastic and silicon. Both the cross-section and average radiative energy loss is reduced in plastic compared to the higher Z silicon.

The GEANT simulations of positrons include radiative energy losses (with a cross-

section as given in Figure AJ), and also track the bremsstrahlung photon to see

if it does get reabsorbed in the plastic before escaping. To correct for differences

in electron and positron cross-sections, GEANT includes a function that scales with

T/Z2 [44]. Earlier cornparisons of measured response functions to (other) GEANT calculations [40) bad the MC consistently underestimating the low-energy tail. Al- though the response function measurements may have some systematic bias from the

e* beam characteristics, the discrepancy is a concern for us because (a) of our sensi-

tivity to the low-energy tail in the /3 - u correlation experirnent and (b) because we

have not experimentally measured the scintillator's response function and are relying

on GEANT to simulate them.

We are presently limited by backgrounds or systematics in our understanding of

the low-energy part of our 38mK spectra, and so c m o t at present use the on-line data

to test GEANT. Once these uncertainties are reduced, an attempt at measuring the

response function for 2-3 MeV positrons may be possibIe dong the slow branch (see

83.1) because the p's energy is slowly varying a t longer times-of-fiight. Reconstruction

of Ep is possible due to the overdetermined kinematics in our geometry; comparison

of the observed and calculated energies for TOF cuts dong the slow branch should at

least provide good estimates of the relative tail-to-total ratios of the response function.

Happily, preliminary calculations 1691 are in agreement with GEANT, but a dedicated

study has yet to be performed.

Annihilation Radiation

Up to now, the effects have been applicable to both electrons and positrons, with

perhaps only minor differences in the details. The response function of positrons will

have additionai components unique to them because they annihilate with free and

atomic electrons.

Compton summing In the case that the positron cornes to rest before annihilating

with a free electron, we know from simple energy-momentum conservation that two back-to-back 7 s will be generated with momenta p,, = -p , and ET, = E, =.me. If these annihilation photons do not interact with the scintillator, then the response is unaffected since the positron deposited al1 of its kinetic energy. However, if one

Compton scatters within the scintillator, then the additional energy deposited by

the Compton scattered electron will be added to the positron's signal. The positron

response will therefore have a high-energy tail extending up to 340 keV from the

full-eaergy peak. Although les likely, both annihilation 7s rnay Compton scatter

cxtending this taii even further, up to 680 keV. This 'Compton toe' is a concern

in the correlation experiment because an improper calculation of this high-energy

Compton tail d l afiect the scintiliator's calibration; the 5.022 MeV end point i d1

appear shifted if too much or not enough Compton sumrning is included.

Annihilation-in-Bight An additionai complication with positrons is the fact that

they can annihilate before coming to rest (annihilation-in-8ight). The ys d l no

longer be back-to-back and E, # E, #me as some of the kinetic energy of the

positron is transferred to annihilation radiation. This t h e , if the annihilation ys

escape the detector, the energy reading will be in the low-energy tail of the response

function because the positron did not deposit al1 of its energy in the detector before annihilating. The cross-section for annihilation into two 7s is given by [70]f

with T, = 2.818 Çi and 7 = E/m,. This cross-section is compared with that of

collisional losses in Figure A.1 and, though it is small compared to ionization losses in our energy range, the integrated probability of annihilation-in-flight is as large as

10% for a 5 MeV positron [711.

t.i\nniLilation to one 7 can occur if the electron is bound, but this cross section goes like (aQ3 compared to a* and so only contributes in hi& Z materiais.

GEANT and Future Work

The success of GEANT in reproducing the observed ,O spectra enables us to place some

trust in its simulations. This coupled with its ease of prograrnming to suit a users

needs has meant it has found applications to other aspects of TRINAT'S potassium

program. Two of these applications, improved geometry designs to reduce scattering

and searching for massive neutrinos, are described below.

B.1 Future geometries

In order to obtain a more uniform and calculable electric field, a redesign of the

electrostatic hoop system is being performed and is hoped to be implemented before

the next running period. Inspired in large part by the scattering effects presented

earlier (see Section 4.5.1), design simulations of the experiment are concurrently being

performed to try to minimize these effects in the new geometry.

One of the major changes to the electric hoops (see Figure B.1) is in the one closest

to the P-telescope. In order to be less sensitive to where ground is defined, this hoop

has been changed into two wide, Bat concentric rings ('hoop 5' and the collimator)

maintaineci at different potentials. On the other side, another end plate ('hoop O*)

has also been added for more uniform fields on the recoil detector's side of the trap.

Then the natural questions became ' m a t sizes (inner diameters and thicknesses) and

materials (Be, Al, W, Ta) should we choose for these new volumes?" The GEANT geometry was amended to include hoop 5 and collimatorso that simulations could help

us to best answer these questions. The geometry was further adapted by T.J. Stocki,

a research associate working with TRINAT, to reflect the rest of the changes in the

FIGURE B.l: Schematic diagram of TRINAT'S new electrostatic hoop design. The changes can be seen by comparing this to Figure 4.7 on page 40.

new electrostatic hoop design, including hoop O and the ceramic rods used to mount

the hoops.

Simulations were run for various dimensions and materials of the collimator and

hoop 5; the MC indicates a factor of two improvement over the geometry presented in

this thesis if a copper-tungsten collimator is used to restrict the cone of ,h from the

trap to hit only the foi1 of the /3 window (and not the steel of the front face). Hoop 5

is made of glassy carbon, and it was found that a number of ps scattered through

it and then into the P-telescope; in an effort to reduce these new scattering effects,

another copper-tungsten collimator (the ' P window collar') was added to the front

face of the scintillator vacuum chamber. The collar extends out far enough that ps

have no solid angle for entering the telescope directly from hoop 5 and greatly reduces

these scattered events.

The material of hoop O was carefully considered because we want to make sure

we minimize backscattering effects. If this plate is also made of glassy carbon, the 0s

have a good probability of transmitting through the plate rather than backscattering;

once through, they readily scatter off the other (higher 2) materials, but the solid

angle for firing the P-telescope is very small.

B.2 MASSIVE NEUTRINOS 119

B.2 Massive neutrinos

The correlation experiment, as mentioned earlier, provides us with the momenta (both

direction and magnitude) of both the recoil and the B from the 3BmK decay. From

these measurements, we can deduce the neutrino momentum on an event-by-event

basis, limited by how well the ef energy is measured. The kinematics of the decay

described in 53.1 (on page 14) assumed a massless neutrino, and indeed we know this

to be tme at the eV level for the v,. The limits on the C( and T neutrino's, however,

are not as stringent and, if they have mass, the observable eigenstates of the weak

interaction can mix with the mass eigenstates. In this case the kinematics of the decay

will be quite different, as depicted in Figure B.2. For the fast branch, where there

are many events, a massive neutrino will take energy away from the recoil to conserve

momentum, resulting in an extra ridge at longer time-of-flight . The separation of this

ridge from the fast branch where no mixing occured will be related to the mass of the heavy neutrino; for a 2 MeV heavy neutrino in the geometry of this experiment, it

corresponds to a shift of approximately 200 ns. The relative population of this ridge compared to that of the regular fast branch is determined by the probability of the

electron neutrino mking with a heavier one (as well as changes in the phase space of

the decay and the angular correlat ion).

With the 38mK decay Q-value of 5.022 MeV, our geometry should be sensitive to

neutrinos in mass range of approximately 1-4 MeV. The analysis, which is the central

part of M. Trinczek's Ph.D. thesis [721, will reconstruct the recoil TOF, assuming a

rnassless neutrino, as a function of Tp bins, and then compare tbis cakulated time with

the observed TOF. The massive neutrinos will be clearly visible as their recoostructed

TOF will be incorrect; for this reason, chey will be far removed in TOF from the fast

branch's peak at TOFOb - TOFdc = O. The overall number of counts in each of the

h o peaks wiii be used to place limits on the mixing strength of v, --+ vh,,,.

In order to be able to accurately fit the (regular) fast branch's peak, a MC simula-

tion must be performed to properly account for (a) various scattering effects, ( i i ) the

h i t e trap and detector sizes, and ( i i à ) the response function of the 0-telescope. MC simulations 1651 where the recoil and positron are tracked with a simple mode1 of ( i )

(at most one scatter) are much faster than GEANT simulations (= 4000~). This fast


- - mv = 1 MeV -- . mw = 3 MeV mv = 2 MeV - m v = 4 M e V

FIGURE 8.2: Kinernatics of 3 8 m ~ decay where the emitted neutrino is massive (dashed lines), for masses m, = 1,2,3 and 4 h4eV; the solid line is m, = O. The position of the heavy neutrino ridges depends on its mass, and the relative intensity of this ndge compared to that of the regular fast branch is related to the mixing strength.

simulation accounts for ( i i ) and includes (iii) by convoluting the generated 0 energy

with GEANT simulations of the telescope's response functiont.

The detailed tracking of the positron using GEANT, however, appears to be es-

sentiai because the fast simulations fail to reproduce the tail of the main TOFOb, - TOFCd, = O peak [731. One major source of the TOF tail is the (back)scattered ps because the reconstnicted TOF d l have a wrong d u e of Op, in the calculations.

The massive neutrino peak, though shifted in TOF from the main peak, will still be

in the tail of the m, = O peak. Analysis of the reconstructed events, which looks

for very small peaks on top of the large zero m a s 'background,' therefore requires

GEANT simulations since they best reproduce the m, = O tails.

The m, > O spectrum shape does not need to be as accurately for the andysis

because it is so small compared to the main m, = O peak. For this reason, the fast

Monte Carlo is being used to generate the massive neutrino events and GEANT is only

tThese tespanse functions m e generated in 1998, and so updating them should help to irnprove the fast MC


be needed to generate the background.

Electronics of the fi-Telescope

A schematic of the electronics diagram for the telescope assembly is depicted in Fig-

ure C.1. Below is a brief overview of the system as a whole.

The DSSSD provides us with 24 Z + 24 jj = 48 energy signals and 6 groups of $

timing signals (consisting of 4 strips each). Each of the 24 y-strip's timing signals have discriminators set to 5 15 keV; if any of the strips p a s this hardware threshold,

the timing signai is used to generate a (wide) DSSSD event trigger. The gain of al1 48 strips is monitored using the Ortec 448 research pulser.

The scintillator energy is taken £rom the dynode output of the PMT after it is

invected by the LeCroy 428F linear fan-in/fan-out. The high voltage applied to the

PMT is adjusted by the stabilization unit based on the LED signals observed; the

intensity of the LED is (independently) maintained constant using a temperature stabilized photodiode. The Tennelec 455 constant fraction discriminator uses the

anode signai to generate the scintiljator's (short) timing signal. The gates for the ADCs and the starts for the TDCs are al1 derived frorn the

LeCroy 429A unit labeiied 'event trigger'. The inputs to this unit, i.e. the various event types, are:

1. A prescaled scintiiiator event,

2. A hardware DSSSD-scintiilator coincidence,

3. DSSSD/MCP pulser events Gom the Ortec 448,

4. Scintillator pulser (LED) events fiom the stabilization unit, and

APPENDM C ELECTRONICS OF THE FTELESCOPE 123

FIGURE (2.1: Electronics diagram for the DSSSD and scintillator.

APPENDIX C ELECTRONICS OF THE ~TELESCOPE 124

5. Event triggers from the MCP (though not generally used on-line because of its

high rates).

The coincidence register (C212) allows us to record which of these generated the

event tcïgger. In addition, this unit is used to define where within the trap cycle a

given eveat took place; the signais are taken from the PC controlling the trap and

tell us when the atoms are being transferred (push beam on/off), if there are atoms

in the trap or if they are being loaded (trap on/off) and what detunings are used in the MOT'S lasersf ('tiny' trap on/ofT).

The CAMAC system is used to acquire the data and is recorded in the YBOS format both on the disk of the host Pentium III 500 MHz Linux PC as well as on

magnetic tapes. Both the on-line and off-line data malysis are done using a TR~uMF standard program [741 with a special subroutine added to incorporate the analysis

scherne of the DSSSD 4.2.5.

tBy changing the detunings once the trap is already loaded, the size of the atom cloud is ceduced.

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